EXHIBIT 1.1



                               UNIT CORPORATION

                              7,000,000 Shares(1)



                                 Common Stock

                            UNDERWRITING AGREEMENT
                            ----------------------

                                                            September 23, 1999

PRUDENTIAL SECURITIES INCORPORATED
CIBC WORLD MARKETS CORP.
RAYMOND JAMES & ASSOCIATES, INC.
As Representatives of the several Underwriters
c/o Prudential Securities Incorporated
One New York Plaza
New York, New York  10292

Dear Sirs:

          Unit Corporation, a Delaware corporation (the "Company"), hereby
confirms its agreement with the several underwriters named in Schedule I hereto
(the "Underwriters"), for whom you have been duly authorized to act as
representatives (in such capacities, the "Representatives"), as set forth below.
If you are the only Underwriters, all references herein to the Representatives
shall be deemed to be to the Underwriters.

     1.   Securities.  Subject to the terms and conditions herein contained, the
          ----------
Company proposes to issue and sell to the several Underwriters an aggregate of
7,000,000 shares (the "Firm Securities") of the Company's Common Stock, par
value $.20 per share ("Common Stock").  The Company also proposes to issue and
sell to the several Underwriters not more than 1,050,000 additional shares of
Common Stock if requested by the Representatives as provided in Section 3 of
this Agreement.  Any and all shares of Common Stock to be purchased by the
Underwriters pursuant to such option are referred to herein as the "Option
Securities", and the Firm Securities and any Option Securities are collectively
referred to herein as the "Securities".

     2.   Representations and Warranties of the Company.  The Company represents
          ----------------------------------------------
and warrants to, and agrees with, each of the several Underwriters that:

          (a) The Company meets the requirements for use of Form S-3 under the
     Securities Act of 1933, as amended (the "Act").  A registration statement
     on such Form (File No. 333-83551) with respect to the Securities, including
     a prospectus subject to completion, has been filed by the Company with the
     Securities and Exchange Commission (the "Commission") under the Act, and

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(1)  Plus an option to purchase from Unit Corporation up to 1,050,000 additional
     shares to cover over-allotments.


     such registration statement has been declared by the Commission to be
     effective under the Act.  Prior to the date hereof, the Company has
     prepared and filed with the Commission pursuant to Rule 424(b) under the
     Act a prospectus supplement reflecting the terms of the Securities, the
     terms of the offering thereof and the other matters set forth therein.
     Such prospectus supplement and any additional prospectus supplements filed
     pursuant to Rule 424(b) under the Act prior to the filing of the prospectus
     supplement included in the Prospectus (as hereinafter defined), together
     with the prospectus included in the Registration Statement, including all
     documents incorporated by reference therein filed under the Securities
     Exchange Act of 1934, as amended (the "Exchange Act"), is referred to as
     the "Preliminary Prospectus."  After the execution of this Agreement, the
     Company will file with the Commission a prospectus supplement in the form
     of the prospectus supplement included in the Preliminary Prospectus with
     such changes or insertions as are permitted by Rule 424(b) under the Act
     and as have been provided to and approved by the Representatives prior to
     the execution of this Agreement.  Such prospectus supplement, together with
     the prospectus included in the Registration Statement, including all
     documents incorporated by reference therein filed under the Exchange Act,
     is referred to as the "Prospectus."  The Company may also file a related
     registration statement with the Commission pursuant to Rule 462(b) under
     the Act for the purpose of registering certain additional Securities, which
     registration shall be effective upon filing with the Commission.  As used
     in this Agreement, the term "Original Registration Statement" means the
     registration statement initially filed relating to the Securities, as
     amended at the time when it was or is declared effective, including (A) all
     financial schedules and exhibits thereto, and (B) all documents
     incorporated by reference therein filed under the Exchange Act; the term
     "Rule 462(b) Registration Statement" means any registration statement filed
     with the Commission pursuant to Rule 462(b) under the Act (including the
     Registration Statement and any Preliminary Prospectus or Prospectus
     incorporated therein at the time such Registration Statement becomes
     effective); and the term "Registration Statement" includes both the
     Original Registration Statement and any Rule 462(b) Registration Statement.
     Any reference in this Agreement to an "amendment or supplement" to any
     Preliminary Prospectus or the Prospectus or an "amendment" to any
     registration statement (including the Registration Statement) shall be
     deemed to include any document incorporated by reference therein that is
     filed with the Commission under the Exchange Act after the date of such
     Preliminary Prospectus, Prospectus or registration statement, as the case
     may be.  For purposes of the preceding sentence, any reference to the
     "effective date" of an amendment to a registration statement shall, if such
     amendment is effected by means of the filing with the Commission under the
     Exchange Act of a document incorporated by reference in such registration
     statement, be deemed to refer to the date on which such document was so
     filed with the Commission.

          (b) The Commission has not issued any order preventing or suspending
     the use of any Preliminary Prospectus.  When any Preliminary Prospectus and
     any amendment or supplement thereto was filed with the Commission, it (i)
     contained all statements required to be stated therein in accordance with,
     and complied in all material respects with the requirements of, the Act,
     the Exchange Act and the respective rules and regulations of the Commission
     thereunder, and (ii) did not include any untrue statement of a material
     fact or omit to state any material fact necessary in order to make the
     statements therein, in the light of the circumstances under which they were
     made, not misleading.  When the Registration Statement or any amendment
     thereto was declared effective, it (i) contained all statements required to
     be stated therein in accordance with, and complied in all material respects
     with the requirements of, the Act, the Exchange Act and the respective
     rules and regulations of the Commission thereunder and (ii) did not include
     any untrue statement of a material fact or omit to state any material fact
     necessary to make the statements therein not misleading.  When the
     Prospectus or any amendment or supplement to the Prospectus is

                                      -2-


     filed with the Commission pursuant to Rule 424(b) and on the Firm Closing
     Date and any Option Closing Date (both as hereinafter defined), the
     Prospectus, as amended or supplemented at any such time, (i) contained or
     will contain all statements required to be stated therein in accordance
     with, and complied or will comply in all material respects with the
     requirements of, the Act, the Exchange Act and the respective rules and
     regulations of the Commission thereunder and (ii) did not or will not
     include any untrue statement of a material fact or omit to state any
     material fact necessary in order to make the statements therein, in the
     light of the circumstances under which they were made, not misleading. The
     documents incorporated by reference in the Prospectus, (i) at the time they
     were filed with the Commission, contained or will contain all statements
     required to be stated therein in accordance with, and complied in all
     material respects with the requirements of, the Exchange Act and the rules
     and regulations of the Commission thereunder, and (ii) when read together
     with the other information in the Prospectus, did not or will not, on the
     date hereof and at the Firm Closing Date and any Option Closing Date,
     include an untrue statement of a material fact or omit to state a material
     fact necessary in order to make the statements therein, in light of the
     circumstances under which they were made, not misleading. The foregoing
     provisions of this paragraph (b) do not apply to statements or omissions
     made in any Preliminary Prospectus or any amendment or supplement thereto,
     the Registration Statement or any amendment thereto, the Prospectus or any
     amendment or supplement thereto in reliance upon and in conformity with
     written information furnished to the Company by any Underwriter through the
     Representatives specifically for use therein.

          (c) If the Company has elected to rely on Rule 462(b) and the Rule
     462(b) Registration Statement has not been declared effective (i) the
     Company has filed a Rule 462(b) Registration Statement in compliance with
     and that is effective upon filing pursuant to Rule 462(b) and has received
     confirmation of its receipt and (ii) the Company has given irrevocable
     instructions for transmission of the applicable filing fee in connection
     with the filing of the Rule 462(b) Registration Statement, in compliance
     with Rule 111 promulgated under the Act or the Commission has received
     payment of such filing fee.

          (d) The Company and each of its subsidiaries have been duly organized
     and are validly existing as corporations, partnerships or limited liability
     companies, as the case may be, in good standing under the laws of their
     respective jurisdictions of incorporation and are duly qualified to
     transact business as foreign corporations, partnerships or limited
     liability companies, as the case may be, and are in good standing under the
     laws of all other jurisdictions where the ownership or leasing of their
     respective properties or the conduct of their respective businesses
     requires such qualification, except where the failure to be so qualified
     does not amount to a material liability or disability to the Company and
     its subsidiaries, taken as a whole.

          (e) The Company and each of its subsidiaries have full power
     (corporate and other) to own or lease their respective properties and
     conduct their respective businesses as described in the Registration
     Statement, the Prospectus or, if the Prospectus is not in existence, the
     most recent Preliminary Prospectus; and the Company has full power
     (corporate and other) to enter into this Agreement and to carry out all the
     terms and provisions hereof to be carried out by it.

          (f) The issued shares of capital stock of each of the Company's
     corporate subsidiaries have been duly authorized and validly issued, are
     fully paid and nonassessable and are owned beneficially by the Company free
     and clear of any security interests, liens, encumbrances, equities or
     claims.  The general partner interests in each of the Company's partnership
     subsidiaries are duly authorized by the partnership agreement of such
     partnership and have been validly issued in

                                      -3-


     accordance with such partnership agreement and are owned beneficially by
     the Company free and clear of any security interests, liens, encumbrances,
     equities or claims. The limited liability company interests owned by the
     Company in each of the Company's limited liability company subsidiaries are
     duly authorized by the organizational documents of such limited liability
     company and have been validly issued in accordance with such organizational
     documents and are owned beneficially by the Company free and clear of any
     security interests, liens, encumbrances, equities or claims.

          (g) The Company has an authorized, issued and outstanding
     capitalization as set forth in the Prospectus or, if the Prospectus is not
     in existence, the most recent Preliminary Prospectus.  All of the issued
     shares of capital stock of the Company have been duly authorized and
     validly issued and are fully paid and nonassessable.  The Firm Securities
     and the Option Securities have been duly authorized and at the Firm Closing
     Date or the related Option Closing Date (as the case may be), after payment
     therefor in accordance herewith, will be validly issued, fully paid and
     nonassessable.  No holders of outstanding shares of capital stock of the
     Company are entitled as such to any preemptive or other rights to subscribe
     for any of the Securities, and no holder of securities of the Company has
     any right which has not been fully exercised or waived to require the
     Company to register the offer or sale of any securities owned by such
     holder under the Act in the public offering contemplated by this Agreement.

          (h) The capital stock of the Company conforms to the description
     thereof contained in the Prospectus or, if the Prospectus is not in
     existence, the most recent Preliminary Prospectus.

          (i) Except as disclosed in the Prospectus or, if the Prospectus is not
     in existence, the most recent Preliminary Prospectus, there are not
     outstanding (A) securities or obligations of the Company or any of its
     subsidiaries convertible into or exchangeable for any capital stock of the
     Company or any such subsidiary, (B) warrants, rights or options to
     subscribe for or purchase from the Company or any such subsidiary any such
     capital stock or any such convertible or exchangeable securities or
     obligations, or (C) obligations of the Company or any such subsidiary to
     issue any shares of capital stock, any such convertible or exchangeable
     securities or obligations, or any such warrants, rights or options.

          (j) The consolidated financial statements and schedules of the Company
     and its consolidated subsidiaries included in the Registration Statement or
     the Prospectus or, if the Prospectus is not in existence, the most recent
     Preliminary Prospectus, fairly present the financial position of the
     Company and its consolidated subsidiaries and the results of operations and
     changes in financial condition as of the dates and periods therein
     specified.  Such financial statements and schedules have been prepared in
     accordance with generally accepted accounting principles consistently
     applied throughout the periods involved (except as otherwise noted
     therein).  The selected financial data set forth under the caption
     "Selected Consolidated Financial Data" in the Prospectus or if the
     Prospectus is not in existence, the most recent Preliminary Prospectus and
     in the Company's Annual Report on Form 10-K for the fiscal year ended
     December 31, 1998, fairly present, on the basis stated in the Prospectus or
     such Preliminary Prospectus and such Annual Report, the information
     included therein.

          (k) PricewaterhouseCoopers LLP, who have certified certain financial
     statements of the Company and its consolidated subsidiaries and delivered
     their report with respect to the audited consolidated financial statements
     and schedules incorporated by reference in the Registration Statement and
     included in the Prospectus (or, if the Prospectus is not in existence, the
     most recent

                                      -4-


     Preliminary Prospectus), are independent public accountants as required by
     the Act, the Exchange Act and the related published rules and regulations
     thereunder.

          (l) Ryder Scott Company, L.P., who have reviewed certain reserve
     estimates of the Company and its consolidated subsidiaries, are independent
     petroleum consultants with respect to the Company.

          (m) The execution and delivery of this Agreement have been duly
     authorized by the Company and this Agreement has been duly executed and
     delivered by the Company, and is the valid and binding agreement of the
     Company, enforceable against the Company in accordance with its terms,
     except as enforceability may be limited by (i) bankruptcy, insolvency,
     reorganization, moratorium or similar laws of general application affecting
     enforcement of creditors' rights, (ii) by application of legal principles
     affecting the availability of equitable remedies, and (iii)by rules,
     statutes or case decisions affecting the availability of indemnification or
     contribution rights hereunder .

          (n) No legal or governmental proceedings are pending to which the
     Company or any of its subsidiaries is a party or to which the property of
     the Company or any of its subsidiaries is subject that are required to be
     described in the Registration Statement or the Prospectus or, if the
     Prospectus is not in existence, the most recent Preliminary Prospectus, and
     no such proceedings have been threatened against the Company or any of its
     subsidiaries or with respect to any of their respective properties; and no
     contract or other document is required to be described in the Registration
     Statement or the Prospectus or to be filed as an exhibit to the
     Registration Statement that is not described therein (or, if the Prospectus
     is not in existence, the most recent Preliminary Prospectus) or filed as
     required.

          (o) The issuance, offering and sale of the Securities to the
     Underwriters by the Company pursuant to this Agreement, the compliance by
     the Company with the other provisions of this Agreement and the
     consummation of the other transactions herein contemplated do not (i)
     require the consent, approval, authorization, registration or qualification
     of or with any governmental authority, except such as have been obtained
     and such as may be required under state securities or blue sky laws, or
     (ii) conflict with or result in a breach or violation of any of the terms
     and provisions of, or constitute a default under, any indenture, mortgage,
     deed of trust, lease or other agreement or instrument to which the Company
     or any of its subsidiaries is a party or by which the Company or any of its
     subsidiaries or any of their respective properties are bound, or the
     charter documents or by-laws of the Company or any of its subsidiaries, or
     any statute or any judgment, decree, order, rule or regulation of any court
     or other governmental authority or any arbitrator applicable to the Company
     or any of its subsidiaries.

          (p) Subsequent to the respective dates as of which information is
     given in the Registration Statement and the Prospectus or, if the
     Prospectus is not in existence, the most recent Preliminary Prospectus,
     neither the Company nor any of its subsidiaries has sustained any material
     loss or interference with their respective businesses or properties from
     fire, flood, hurricane, accident or other calamity, whether or not covered
     by insurance, or from any labor dispute or any legal or governmental
     proceeding and there has not been any material adverse change, or any
     development involving a prospective material adverse change, in the
     condition (financial or otherwise), management, business prospects, net
     worth, or results of operations of the Company or any of its subsidiaries,
     except in each case as described in or contemplated by the Prospectus or,
     if the Prospectus is not in existence, the most recent Preliminary
     Prospectus.

                                      -5-


          (q) The Company has not, directly or indirectly, (i) taken any action
     designed to cause or to result in, or that has constituted or which might
     reasonably be expected to constitute, the stabilization or manipulation of
     the price of any security of the Company to facilitate the sale or resale
     of the Securities or (ii) since the filing of the Registration Statement
     (A) sold, bid for, purchased, or paid anyone any compensation for
     soliciting purchases of, the Securities or (B) paid or agreed to pay to any
     person any compensation for soliciting another to purchase any other
     securities of the Company.

          (r) The Company has not distributed and, prior to the later of (i) the
     Firm Closing Date and the Option Closing Date and (ii) the completion of
     the distribution of the Securities, will not distribute any offering
     material in connection with the offering and sale of the Securities other
     than the Registration Statement or any amendment thereto, any Preliminary
     Prospectus or the Prospectus or any amendment or supplement thereto, or
     other materials, if any, permitted by the Act.

          (s) Subsequent to the respective dates as of which information is
     given in the Registration Statement and the Prospectus (or, if the
     Prospectus is not in existence, the most recent Preliminary Prospectus),
     (1) the Company and its subsidiaries have not incurred any material
     liability or obligation, direct or contingent, nor entered into any
     material transaction not in the ordinary course of business; (2) the
     Company has not purchased any of its outstanding capital stock, nor
     declared, paid or otherwise made any dividend or distribution of any kind
     on its capital stock; and (3) there has not been any material change in the
     capital stock, short-term debt or long-term debt of the Company and its
     consolidated subsidiaries, except in each case as described in or
     contemplated by the Prospectus (or, if the Prospectus is not in existence,
     the most recent Preliminary Prospectus).

          (t) The Company and each of its subsidiaries have good and marketable
     title in fee simple to all items of real property and marketable title to
     all personal property owned by each of them, in each case free and clear of
     any security interests, liens, encumbrances, equities, claims and other
     defects, except for security interests and other liens securing the
     Company's drilling rigs and related equipment and such other security
     interests, liens, encumbrances, equities, claims and other defects as do
     not materially and adversely affect the value of such property and do not
     interfere with the use made or proposed to be made of such property by the
     Company or such subsidiary, and any real property and buildings held under
     lease by the Company or any such subsidiary are held under valid,
     subsisting and enforceable leases, with such exceptions as are not material
     and do not interfere with the use made or proposed to be made of such
     property and buildings by the Company or such subsidiary, in each case
     except as described in or contemplated by the Prospectus (or, if the
     Prospectus is not in existence, the most recent Preliminary Prospectus).

          (u) No labor dispute with the employees of the Company or any of its
     subsidiaries exists or is threatened or imminent that could result in a
     material adverse change in the condition (financial or otherwise), business
     prospects, net worth or results of operations of the Company and its
     subsidiaries, except as described in or contemplated by the Prospectus (or,
     if the Prospectus is not in existence, the most recent Preliminary
     Prospectus).

          (v) The Company and its subsidiaries own or possess, or can acquire on
     reasonable terms, all material patents, patent applications, trademarks,
     service marks, trade names, licenses,

                                      -6-


     copyrights and proprietary or other confidential information currently
     employed by them in connection with their respective businesses, and
     neither the Company nor any such subsidiary has received any notice of
     infringement of or conflict with asserted rights of any third party with
     respect to any of the foregoing which, singly or in the aggregate, if the
     subject of an unfavorable decision, ruling or finding, would result in a
     material adverse change in the condition (financial or otherwise), business
     prospects, net worth or results of operations of the Company and its
     subsidiaries, except as described in or contemplated by the Prospectus (or,
     if the Prospectus is not in existence, the most recent Preliminary
     Prospectus).

          (w) The Company and each of its subsidiaries are insured by insurers
     of recognized financial responsibility against such losses and risks and in
     such amounts as are prudent and customary in the businesses in which they
     are engaged; neither the Company nor any such subsidiary has been refused
     any insurance coverage sought or applied for; and neither the Company nor
     any such subsidiary has any reason to believe that it will not be able to
     renew its existing insurance coverage as and when such coverage expires or
     to obtain similar coverage from similar insurers as may be necessary to
     continue its business at a cost that would not materially and adversely
     affect the condition (financial or otherwise), business prospects, net
     worth or results of operations of the Company and its subsidiaries, except
     as described in or contemplated by the Prospectus (or, if the Prospectus is
     not in existence, the most recent Preliminary Prospectus).

          (x) No subsidiary of the Company is currently prohibited, directly or
     indirectly, from paying any dividends to the Company, from making any other
     distribution on such subsidiary's capital stock, from repaying to the
     Company any loans or advances to such subsidiary from the Company or from
     transferring any of such subsidiary's property or assets to the Company or
     any other subsidiary of the Company, except as described in or contemplated
     by the Prospectus (or, if the Prospectus is not in existence, the most
     recent Preliminary Prospectus).

          (y) The Company and its subsidiaries possess all certificates,
     authorizations and permits issued by the appropriate federal, state or
     foreign regulatory authorities necessary to conduct their respective
     businesses, and neither the Company nor any such subsidiary has received
     any notice of proceedings relating to the revocation or modification of any
     such certificate, authorization or permit which, singly or in the
     aggregate, if the subject of an unfavorable decision, ruling or finding,
     would result in a material adverse change in the condition (financial or
     otherwise), business prospects, net worth or results of operations of the
     Company and its subsidiaries, except as described in or contemplated by the
     Prospectus (or, if the Prospectus is not in existence, the most recent
     Preliminary Prospectus).

          (z) The Company will conduct its operations in a manner that will not
     subject it to registration as an investment company under the Investment
     Company Act of 1940, as amended, and this transaction will not cause the
     Company to become an investment company subject to registration under such
     Act.

          (aa) The Company has filed all foreign, federal, state and local tax
     returns that are required to be filed or has requested extensions thereof
     (except in any case in which the failure so to file would not have a
     material adverse effect on the Company and its subsidiaries) and has paid
     all taxes required to be paid by it and any other assessment, fine or
     penalty levied against it, to the extent that any of the foregoing is due
     and payable, except for any such assessment, fine or

                                      -7-


     penalty that is currently being contested in good faith or as described in
     or contemplated by the Prospectus (or, if the Prospectus is not in
     existence, the most recent Preliminary Prospectus).

          (bb) Neither the Company nor any of its subsidiaries is in violation
     of any federal or state law or regulation relating to occupational safety
     and health or to the storage, handling or transportation of hazardous or
     toxic materials and the Company and its subsidiaries have received all
     permits, licenses or other approvals required of them under applicable
     federal and state occupational safety and health and environmental laws and
     regulations to conduct their respective businesses, and the Company and
     each such subsidiary is in compliance with all terms and conditions of any
     such permit, license or approval, except any such violation of law or
     regulation, failure to receive required permits, licenses or other
     approvals or failure to comply with the terms and conditions of such
     permits, licenses or approvals which would not, singly or in the aggregate,
     result in a material adverse change in the condition (financial or
     otherwise), business prospects, net worth or results of operations of the
     Company and its subsidiaries, except as described in or contemplated by the
     Prospectus (or, if the Prospectus is not in existence, the most recent
     Preliminary Prospectus).

          (cc) Each certificate signed by any officer of the Company and
     delivered to the Representatives or counsel for the Underwriters shall be
     deemed to be a representation and warranty by the Company to each
     Underwriter as to the matters covered thereby.

          (dd) Except for the shares of capital stock of each of the
     subsidiaries owned by the Company and such subsidiaries, neither the
     Company nor any such subsidiary owns any shares of stock or any other
     equity securities of any corporation or has any equity interest in any
     firm, partnership, association or other entity, except as described in or
     contemplated by the Prospectus (or, if the Prospectus is not in existence,
     the most recent Preliminary Prospectus).  Unit Drilling Company, Unit
     Petroleum Company and Petroleum Supply Company are the only significant
     subsidiaries of the Company within the meaning of Rule 12b-2 under the
     Exchange Act.

          (ee) There are no holders of securities of the Company, who, by reason
     of the filing of the Registration Statement, have the right (and have not
     waived such right) to request the Company to register under the Act, or to
     include in the Registration Statement, securities held by them.

          (ff) The Company and each of its subsidiaries maintain a system of
     internal accounting controls sufficient to provide reasonable assurance
     that (1) transactions are executed in accordance with management's general
     or specific authorizations; (2) transactions are recorded as necessary to
     permit preparation of financial statements in conformity with generally
     accepted accounting principles and to maintain asset accountability; (3)
     access to assets is permitted only in accordance with management's general
     or specific authorization; and (4) the recorded accountability for assets
     is compared with the existing assets at reasonable intervals and
     appropriate action is taken with respect to any differences.

          (gg) No default exists, and no event has occurred which, with notice
     or lapse of time or both, would constitute a default in the due performance
     and observance of any term, covenant or condition of any indenture,
     mortgage, deed of trust, lease or other agreement or instrument to which
     the Company or any of its subsidiaries is a party or by which the Company
     or any of its subsidiaries or any of their respective properties is bound
     or may be affected in any material

                                      -8-


     adverse respect with regard to property, business or operations of the
     Company and its subsidiaries.

       3.  Purchase, Sale and Delivery of the Securities. (a) On the basis of
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     the representations, warranties, agreements and covenants herein contained
     and subject to the terms and conditions herein set forth, the Company
     agrees to issue and sell to each of the Underwriters, and each of the
     Underwriters, severally and not jointly, agrees to purchase from the
     Company, at a purchase price of $7.205 per share, the number of Firm
     Securities set forth opposite the name of such Underwriter in Schedule 1
     hereto.  One or more certificates in definitive form for the Firm
     Securities that the several Underwriters have agreed to purchase hereunder,
     and in such denomination or denominations and registered in such name or
     names as the Representatives request upon notice to the Company at least 48
     hours prior to the Firm Closing Date, shall be delivered by or on behalf of
     the Company to the Representatives for the respective accounts of the
     Underwriters, against payment by or on behalf of the Underwriters of the
     purchase price therefor by wire transfer in same-day funds (the "Wired
     Funds") to the account of the Company.  Such delivery of and payment for
     the Firm Securities shall be made at the offices of Baker & Botts, L.L.P.,
     3000 One Shell Plaza, 910 Louisiana, Houston, Texas 77002, at 9:30 A.M.,
     New York time, on September 29, 1999, or at such other place, time or date
     as the Representatives and the Company may agree upon or as the
     Representatives may determine pursuant to Section 9 hereof, such time and
     date of delivery against payment being herein referred to as the "Firm
     Closing Date".  The Company will make such certificate or certificates for
     the Firm Securities available for checking and packaging by the
     Representatives at the offices in New York, New York of the Company's
     transfer agent or registrar or of Prudential Securities Incorporated at
     least 24 hours prior to the Firm Closing Date.

          (b) For the purpose of covering any over-allotments in connection with
     the distribution and sale of the Firm Securities as contemplated by the
     Prospectus, the Company hereby grants to the several Underwriters an option
     to purchase, severally and not jointly, the Option Securities.  The
     purchase price to be paid for any Option Securities shall be the same price
     per share as the price per share for the Firm Securities set forth above in
     paragraph (a) of this Section 3.  The option granted hereby may be
     exercised as to all or any part of the Option Securities from time to time
     within thirty days after the date of the Prospectus (or, if such 30th day
     shall be a Saturday or Sunday or a holiday, on the next business day
     thereafter when the New York Stock Exchange is open for trading).  The
     Underwriters shall not be under any obligation to purchase any of the
     Option Securities prior to the exercise of such option.  The
     Representatives may from time to time exercise the option granted hereby by
     giving notice in writing or by telephone (confirmed in writing) to the
     Company setting forth the aggregate number of Option Securities as to which
     the several Underwriters are then exercising the option and the date and
     time for delivery of and payment for such Option Securities.  Any such date
     of delivery shall be determined by the Representatives but shall not be
     earlier than two business days or later than five business days after such
     exercise of the option and, in any event, shall not be earlier than the
     Firm Closing Date.  The time and date set forth in such notice, or such
     other time on such other date as the Representatives and the Company may
     agree upon or as the Representatives may determine pursuant to Section 9
     hereof, is herein called the "Option Closing Date" with respect to such
     Option Securities.  Upon exercise of the option as provided herein, the
     Company shall become obligated to sell to each of the several Underwriters,
     and, subject to the terms and conditions herein set forth, each of the
     Underwriters (severally and not jointly) shall become obligated to purchase
     from the Company, the same percentage of the total number of the Option
     Securities as to which the several Underwriters are then exercising the
     option as such Underwriter is obligated to purchase of the aggregate number
     of Firm Securities, as adjusted by the Representatives in such manner as
     they deem advisable to

                                      -9-


     avoid fractional shares. If the option is exercised as to all or any
     portion of the Option Securities, one or more certificates in definitive
     form for such Option Securities, and payment therefor, shall be delivered
     on the related Option Closing Date in the manner, and upon the terms and
     conditions, set forth in paragraph (a) of this Section 3, except that
     reference therein to the Firm Securities and the Firm Closing Date shall be
     deemed, for purposes of this paragraph (b), to refer to such Option
     Securities and Option Closing Date, respectively.

          (c) The Company hereby acknowledges that the wire transfer by or on
     behalf of the Underwriters of the purchase price for any Securities does
     not constitute closing of a purchase and sale of the Securities.  Only
     execution and delivery of a receipt for Securities by the Underwriters
     indicates completion of the closing of a purchase of the Securities from
     the Company.  Furthermore, in the event that the Underwriters wire funds to
     the Company prior to the completion of the closing of a purchase of
     Securities, the Company hereby acknowledges that until the Underwriters
     execute and deliver a receipt for the Securities, by facsimile or
     otherwise, the Company will not be entitled to the Wired Funds and shall
     return the Wired Funds to the Underwriters as soon as practicable (by wire
     transfer of same-day funds) upon demand.  In the event that the closing of
     a purchase of Securities is not completed and the Wired Funds are not
     returned by the Company to the Underwriters on the same day the Wired Funds
     were received by the Company, the Company agrees to pay to the Underwriters
     in respect of each day the Wired Funds are not returned by it, in same-day
     funds, interest on the amount of such Wired Funds in an amount representing
     the Underwriters' cost of financing as reasonably determined by Prudential
     Securities Incorporated.

          (d) It is understood that any of you, individually and not as one of
     the Representatives, may (but shall not be obligated to) make payment on
     behalf of any Underwriter or Underwriters for any of the Securities to be
     purchased by such Underwriter or Underwriters.  No such payment shall
     relieve such Underwriter or Underwriters from any of its or their
     obligations hereunder.

     4.   Offering by the Underwriters.  Upon your authorization of the release
          ----------------------------
of the Firm Securities, the several Underwriters propose to offer the Firm
Securities for sale to the public upon the terms set forth in the Prospectus.

     5.   Covenants of the Company.  The Company covenants and agrees with each
          ------------------------
of the Underwriters that:

          (a) The Company will use its best efforts to cause the Registration
     Statement, if not effective at the time of execution of this Agreement, and
     any amendments thereto to become effective as promptly as possible.  If
     required, the Company will file the Prospectus and any amendment or
     supplement thereto with the Commission in the manner and within the time
     period required by Rules 434 and 424(b) under the Act.  During any time
     when a prospectus relating to the Securities is required to be delivered
     under the Act, the Company (i) will comply with all requirements imposed
     upon it by the Act, the Exchange Act and the respective rules and
     regulations of the Commission thereunder to the extent necessary to permit
     the continuance of sales of or dealings in the Securities in accordance
     with the provisions hereof and the Prospectus, as then amended or
     supplemented, and (ii) will not file with the Commission the Prospectus,
     any amendment or supplement to such Prospectus or any amendment to the
     Registration Statement or any Rule 462(b) Registration Statement of which
     the Representatives shall not previously have been advised and furnished
     with a copy for a reasonable period of time prior to the proposed filing
     and as to which filing the Representatives shall not have given their
     consent.  The Company will

                                      -10-


     prepare and file with the Commission, in accordance with the rules and
     regulations of the Commission, promptly upon request by the Representatives
     or counsel for the Underwriters, any amendments to the Registration
     Statement or amendments or supplements to the Prospectus that may be
     necessary or advisable in connection with the distribution of the
     Securities by the several Underwriters, and will use its best efforts to
     cause any such amendment to the Registration Statement to be declared
     effective by the Commission as promptly as possible. The Company will
     advise the Representatives, promptly after receiving notice thereof, of the
     time when the Registration Statement or any amendment thereto has been
     filed or declared effective or the Prospectus or any amendment or
     supplement thereto has been filed and will provide evidence satisfactory to
     the Representatives of each such filing or effectiveness.

          (b) The Company will advise the Representatives, promptly after
     receiving notice or obtaining knowledge thereof, of (i) the issuance by the
     Commission of any stop order suspending the effectiveness of the Original
     Registration Statement or any Rule 462(b) Registration Statement or any
     post-effective amendment thereto or any order directed at any document
     incorporated by reference in the Registration Statement or the Prospectus
     or any amendment or supplement thereto or any order preventing or
     suspending the use of any Preliminary Prospectus, the Prospectus or any
     amendment or supplement thereto, (ii) the suspension of the qualification
     of the Securities for offering or sale in any jurisdiction, (iii) the
     institution, threatening or contemplation of any proceeding for any such
     purpose or (iv) any request made by the Commission for amending the
     Original Registration Statement or any Rule 462(b) Registration Statement,
     for amending or supplementing any Preliminary Prospectus or the Prospectus
     or for additional information.  The Company will use its best efforts to
     prevent the issuance of any such stop order and, if any such stop order is
     issued, to obtain the withdrawal thereof as promptly as possible.

          (c) The Company will arrange for the qualification of the Securities
     for offering and sale under the securities or blue sky laws of such
     jurisdictions as the Representatives may designate and will continue such
     qualifications in effect for as long as may be necessary to complete the
     distribution of the Securities, provided, however, that in connection
                                     -----------------
     therewith the Company shall not be required to qualify as a foreign
     corporation or to execute a general consent to service of process in any
     jurisdiction.

          (d) If, at any time prior to the later of (i) the final date when a
     prospectus relating to the Securities is required to be delivered under the
     Act or (ii) the Option Closing Date, any event occurs as a result of which
     the Prospectus, as then amended or supplemented, would include any untrue
     statement of a material fact or omit to state a material fact necessary in
     order to make the statements therein, in the light of the circumstances
     under which they were made, not misleading, or if for any other reason it
     is necessary at any time to amend or supplement the Prospectus to comply
     with the Act, the Exchange Act or the respective rules or regulations of
     the Commission thereunder, the Company will promptly notify the
     Representatives thereof and, subject to Section 5(a) hereof, will prepare
     and file with the Commission, at the Company's expense, an amendment to the
     Registration Statement or an amendment or supplement to the Prospectus that
     corrects such statement or omission or effects such compliance.

          (e) The Company will, without charge, provide (i) to the
     Representatives and to counsel for the Underwriters a conformed copy of the
     registration statement originally filed with respect to the Securities and
     each amendment thereto (in each case including exhibits thereto) or any
     Rule 462(b) Registration Statement, certified by the Secretary or an
     Assistant Secretary of the Company to be true and complete copies thereof
     as filed with the Commission by electronic

                                      -11-


     transmission, (ii) to each other Underwriter, a conformed copy of such
     registration statement or any Rule 462(b) Registration Statement and each
     amendment thereto (in each case without exhibits thereto) and (iii) so long
     as a prospectus relating to the Securities is required to be delivered
     under the Act, as many copies of each Preliminary Prospectus, the
     Prospectus or any amendment or supplement thereto as the Representatives
     may reasonably request; without limiting the application of clause (iii) of
     this sentence, the Company, not later than (A) 6:00 PM, New York City time,
     on the date of determination of the public offering price, if such
     determination occurred at or prior to 10:00 AM, New York City time on such
     date or (B) 2:00 PM, New York City time, on the business day following the
     date of determination of the public offering price, if such determination
     occurred after 10:00 AM, New York City time, on such date, will deliver to
     the Underwriters, without charge, as many copies of the Prospectus and any
     amendment or supplement thereto as the Representatives may reasonably
     request for purposes of confirming orders that are expected to settle on
     the Firm Closing Date.

          (f) The Company, as soon as practicable, will make generally available
     to its securityholders and to the Representatives a consolidated earnings
     statement of the Company and its subsidiaries that satisfies the provisions
     of Section 11(a) of the Act and Rule 158 thereunder.

          (g) The Company will apply the net proceeds from the sale of the
     Securities as set forth under "Use of Proceeds" in the Prospectus.

          (h) The Company will not, directly or indirectly, without the prior
     written consent of Prudential Securities Incorporated, on behalf of the
     Underwriters, offer, sell, offer to sell, contract to sell, pledge, grant
     any option to purchase or otherwise sell or dispose (or announce any offer,
     sale, offer of sale, contract of sale, pledge, grant of any option to
     purchase or other sale or disposition) of any shares of Common Stock or any
     securities convertible into, or exchangeable or exercisable for, shares of
     Common Stock for a period of 90 days after the date hereof, except pursuant
     to this Agreement, to complete the acquisition of drilling rigs from Parker
     Drilling Company and its subsidiary pursuant to the terms of that certain
     Asset Purchase Agreement dated August 12, 1999 as in effect on the date
     hereof and except for issuances pursuant to the exercise of employee stock
     options outstanding on the date hereof.

          (i) The Company will not, directly or indirectly, (i) take any action
     designed to cause or to result in, or that has constituted or which might
     reasonably be expected to constitute, the stabilization or manipulation of
     the price of any security of the Company to facilitate the sale or resale
     of the Securities or (ii) (A) sell, bid for, purchase, or pay anyone any
     compensation for soliciting purchases of, the Securities or (B) pay or
     agree to pay to any person any compensation for soliciting another to
     purchase any other securities of the Company.

          (j) The Company will obtain the agreements described in Section 7(g)
     hereof prior to the Firm Closing Date.

          (k) If at any time during the 25-day period after the Registration
     Statement becomes effective or the period prior to the Option Closing Date,
     any rumor, publication or event relating to or affecting the Company shall
     occur as a result of which in your opinion the market price of the Common
     Stock has been or is likely to be materially affected (regardless of
     whether such rumor, publication or event necessitates a supplement to or
     amendment of the Prospectus), the Company will, after notice from you
     advising the Company to the effect set forth above, forthwith prepare,
     consult with you concerning the substance of, and disseminate a press
     release or other public

                                      -12-


     statement, reasonably satisfactory to you, responding to or commenting on
     such rumor, publication or event.

          (l) If the Company elects to rely on Rule 462(b), the Company shall
     both file a Rule 462(b) Registration Statement with the Commission in
     compliance with Rule 462(b) and pay the applicable fees in accordance with
     Rule 111 promulgated under the Act by the earlier of (i) 10:00 P.M. Eastern
     time on the date of this Agreement and (ii) the time confirmations are sent
     or given, as specified by Rule 462(b)(2).

          (m) The Company will cause the Securities to be duly authorized for
     listing by the New York Stock Exchange prior to the Firm Closing Date.  The
     Company will ensure that the Securities remain authorized for listing on
     the New York Stock Exchange following the Firm Closing Date.

    6.   Expenses.  The Company will pay all costs and expenses incident to the
         --------
performance of its obligations under this Agreement, whether or not the
transactions contemplated herein are consummated or this Agreement is terminated
pursuant to Section 11 hereof, including all costs and expenses incident to (i)
the printing or other production of documents with respect to the transactions,
including any costs of printing the registration statement originally filed with
respect to the Securities and any amendment thereto, any Rule 462(b)
Registration Statement, any Preliminary Prospectus, the Prospectus and any
amendment or supplement thereto, this Agreement and any blue sky memoranda, (ii)
all arrangements relating to the delivery to the Underwriters of copies of the
foregoing documents, (iii) the fees and disbursements of the counsel,
accountants and any other experts or advisors retained by the Company, (iv)
preparation, issuance and delivery to the Underwriters of any certificates
evidencing the Securities, including transfer agent's and registrar's fees, (v)
the qualification of the Securities under state securities and blue sky laws,
including filing fees and fees and disbursements of counsel for the Underwriters
relating thereto, (vi) the filing fees of the Commission (and the National
Association of Securities Dealers, Inc.) relating to the Securities, (vii) the
listing of the Securities on the New York Stock Exchange, (viii) meetings with
prospective investors in the Securities (other than shall have been specifically
approved by the Representatives to be paid for by the Underwriters) and (ix)
advertising relating to the offering of the Securities (other than shall have
been specifically approved by the Representatives to be paid for by the
Underwriters).  If the sale of the Securities provided for herein is not
consummated because any condition to the obligations of the Underwriters set
forth in Section 7 hereof is not satisfied, because this Agreement is terminated
pursuant to Section 11 hereof or because of any failure, refusal or inability on
the part of the Company to perform all obligations and satisfy all conditions on
its part to be performed or satisfied hereunder other than by reason of a
default by any of the Underwriters, the Company will reimburse the Underwriters
severally upon demand for all out-of-pocket expenses (including fees and
disbursements of counsel) that shall have been incurred by them in connection
with the proposed purchase and sale of the Securities.  The Company shall not in
any event be liable to any of the Underwriters for the loss of anticipated
profits from the transactions covered by this Agreement.

    7.   Conditions of the Underwriters' Obligations.  The obligations of the
         -------------------------------------------
several Underwriters to purchase and pay for the Firm Securities shall be
subject, in the Representatives' sole discretion, to the accuracy of the
representations and warranties of the Company contained herein as of the date
hereof and as of the Firm Closing Date, as if made on and as of the Firm Closing
Date, to the accuracy of the statements of the Company's officers made pursuant
to the provisions hereof, to the performance by the Company of its covenants and
agreements hereunder and to the following additional conditions:

          (a) If the Original Registration Statement or any amendment thereto
     filed prior to the Firm Closing Date has not been declared effective as of
     the time of execution hereof, Original

                                      -13-


     Registration Statement or such amendment and, if the Company has elected to
     rely upon Rule 462(b), the Rule 462(b) Registration Statement shall have
     been declared effective not later than the earlier of (i) 11:00 A.M., New
     York time, on the date on which the amendment to the registration statement
     originally filed with respect to the Securities or to the Registration
     Statement, as the case may be, containing information regarding the initial
     public offering price of the Securities has been filed with the Commission
     and (ii) the time confirmations are sent or given as specified by Rule
     462(b)(2), or with respect to the Original Registration Statement, or such
     later time and date as shall have been consented to by the Representatives;
     if required, the Prospectus and any amendment or supplement thereto shall
     have been filed with the Commission in the manner and within the time
     period required by Rule 434 and 424(b) under the Act; no stop order
     suspending the effectiveness of the Registration Statement or any post-
     effective amendment thereto and no order directed at any document
     incorporated by reference in the Registration Statement, the Prospectus or
     any amendment or supplement thereto shall have been issued and no
     proceedings for that purpose shall have been instituted or threatened or,
     to the knowledge of the Company or the Representatives, shall be
     contemplated by the Commission; and the Company shall have complied with
     any request of the Commission for additional information (to be included in
     the Registration Statement or the Prospectus or otherwise).

          (b) The Representatives shall have received an opinion, dated the Firm
     Closing Date, of Conner & Winters, A Professional Corporation, counsel for
     the Company, to the effect that:

               (i)    the Company and each of Unit Drilling Company, Unit
          Petroleum Company and Petroleum Supply Company (the "Subsidiaries")
          have been duly incorporated and are validly existing as corporations
          in good standing under the laws of their respective jurisdictions of
          incorporation and are duly qualified to transact business as foreign
          corporations and are in good standing under the laws of all other
          jurisdictions where the ownership or leasing of their respective
          properties or the conduct of their respective businesses requires such
          qualification, except where the failure to be so qualified does not
          amount to a material liability or disability to the Company and the
          Subsidiaries, taken as a whole;

               (ii)   the Company and each of the Subsidiaries have corporate
          power to own or lease their respective properties and conduct their
          respective businesses as described in the Registration Statement and
          the Prospectus, and the Company has corporate power to enter into this
          Agreement and to carry out all the terms and provisions hereof to be
          carried out by it;

               (iii)  the issued shares of capital stock of each of the
          Subsidiaries have been duly authorized and validly issued, are fully
          paid and nonassessable and are owned beneficially by the Company free
          and clear of any perfected security interests or, to the best
          knowledge of such counsel, any other security interests, liens,
          encumbrances, equities or claims;

               (iv)   the Company has an authorized, issued and outstanding
          capitalization as set forth in the Prospectus; all of the issued
          shares of capital stock of the Company have been duly authorized and
          validly issued and are fully paid and nonassessable, have been issued
          in compliance with all applicable federal and state securities laws
          and were not issued in violation of or subject to any preemptive
          rights or other rights to subscribe for or purchase securities; the
          Firm Securities have been duly authorized by all necessary

                                      -14-


          corporate action of the Company and, when issued and delivered to and
          paid for by the Underwriters pursuant to this Agreement, will be
          validly issued, fully paid and nonassessable; the Securities have been
          duly authorized for listing, subject to official notice of issuance,
          on the New York Stock Exchange; no holders of outstanding shares of
          capital stock of the Company are entitled as such to any preemptive or
          other rights to subscribe for any of the Securities; and no holders of
          securities of the Company are entitled to have such securities
          registered under the Registration Statement;

               (v)     the statements set forth under the heading "Description
          of Capital Stock" in the Prospectus, insofar as such statements
          purport to summarize certain provisions of the capital stock of the
          Company, provide a fair summary of such provisions; and the statements
          set forth under the headings "Business-Government Regulations,"
          "Business--Federal and State Environmental Regulation," "Shares
          Eligible for Future Sale" and "Description of Capital Stock" in the
          Prospectus, insofar as such statements constitute a summary of the
          legal matters, documents or proceedings referred to therein, provide a
          fair summary of such legal matters, documents and proceedings,

               (vi)    the execution and delivery of this Agreement have been
          duly authorized by all necessary corporate action of the Company and
          this Agreement has been duly executed and delivered by the Company;

               (vii)   no legal or governmental proceedings are pending to which
          the Company or any of the subsidiaries is a party or to which the
          property of the Company or any of the subsidiaries is subject that are
          required to be described in the Registration Statement or the
          Prospectus and are not described therein, and, to the best knowledge
          of such counsel, no such proceedings have been threatened against the
          Company or any of the subsidiaries or with respect to any of their
          respective properties; and no contract or other document is required
          to be described in the Registration Statement and the Prospectus or to
          be filed as an exhibit to the Registration Statement that is not
          described therein or filed as required;

               (viii)  the issuance, offering and sale of the Securities to the
          Underwriters by the Company pursuant to this Agreement, the compliance
          by the Company with the other provisions of this Agreement and the
          consummation of the other transactions herein contemplated do not (A)
          require the consent, approval, authorization, registration or
          qualification of or with any governmental authority, except such as
          have been obtained and such as may be required under state securities
          or blue sky laws, or (B) conflict with or result in a breach or
          violation of any of the terms and provisions of, or constitute a
          default under, any indenture, mortgage, deed of trust, lease or other
          agreement or instrument, known to such counsel, to which the Company
          or any of the subsidiaries is a party or by which the Company or any
          of the subsidiaries or any of their respective properties are bound,
          or the charter documents or by-laws of the Company or any of the
          subsidiaries, or any statute or any judgment, decree, order, rule or
          regulation of any court or other governmental authority or any
          arbitrator known to such counsel and applicable to the Company or any
          of the subsidiaries;

               (ix)    the Registration Statement is effective under the Act;
          any required filing of the Prospectus, pursuant to Rules 434 and
          424(b) has been made in the manner and within the time period required
          by Rules 434 and 424(b); and no stop order suspending the
          effectiveness of the Registration Statement or any post-effective
          amendment thereto and no

                                      -15-


          order directed at any document incorporated by reference in the
          Registration Statement, the Prospectus or any amendment or supplement
          thereto has been issued, and no proceedings for that purpose have been
          instituted or threatened or, to the best knowledge of such counsel,
          are contemplated by the Commission;

               (x)  the Registration Statement originally filed with respect to
          the Securities and each amendment thereto and any Rule 462(b)
          Registration Statement and the Prospectus (in each case, including the
          documents incorporated by reference therein but not including the
          financial statements and other financial information contained
          therein, as to which such counsel need express no opinion) comply as
          to form in all material respects with the applicable requirements of
          the Act, the Exchange Act and the respective rules and regulations of
          the Commission thereunder; and

               (xi) if the Company elects to rely on Rule 434, the Prospectus is
          not "materially different", as such term is used in Rule 434, from the
          prospectus included in the Registration Statement at the time of its
          effectiveness or any effective post-effective amendment thereto
          (including such information that is permitted to be omitted pursuant
          to Rule 430A).

Such counsel shall also state that they have no reason to believe that the
Registration Statement, as of its effective date, contained any untrue statement
of a material fact or omitted to state any material fact required to be stated
therein or necessary to make the statements therein not misleading or that the
Prospectus, as of its date or the date of such opinion, included or includes any
untrue statement of a material fact or omitted or omits to state a material fact
necessary in order to make the statements therein, in the light of the
circumstances under which they were made, not misleading.

    In rendering any such opinion, such counsel may rely, as to matters of fact,
to the extent such counsel deems proper, on certificates of responsible officers
of the Company and public officials.

    References to the Registration Statement and the Prospectus in this
paragraph (b) shall include any amendment or supplement thereto at the date of
such opinion.

          (c) The Representatives shall have received an opinion, dated the Firm
     Closing Date, of Baker & Botts, L.L.P., counsel for the Underwriters, with
     respect to the issuance and sale of the Firm Securities, the Registration
     Statement, the Prospectus and such other related matters as the
     Representatives may reasonably require, and the Company shall have
     furnished to such counsel such documents as they may reasonably request for
     the purpose of enabling them to pass upon such matters. In rendering such
     opinion, such counsel may rely as to all matters of law upon the opinion
     referred to in paragraph (b) above.

          (d) The Representatives shall have received from
     PricewaterhouseCoopers LLP, a letter or letters dated, respectively, the
     date hereof and the Firm Closing Date, in form and substance satisfactory
     to the Representatives, to the effect that:

               (i) they are independent accountants with respect to the Company
          and its consolidated subsidiaries within the meaning of the Act, the
          Exchange Act and the applicable rules and regulations thereunder;

                                      -16-


               (ii)   in their opinion, the audited consolidated financial
          statements and schedules examined by them and included or incorporated
          by reference in the Registration Statement and the Prospectus comply
          in form in all material respects with the applicable accounting
          requirements of the Act, the Exchange Act and the related published
          rules and regulations thereunder;

               (iii)  on the basis of their limited review in accordance with
          standards established by the American Institute of Certified Public
          Accountants of any interim unaudited consolidated condensed financial
          statements of the Company and its consolidated subsidiaries as
          indicated in their reports incorporated in the Registration Statement
          and the Prospectus carrying out certain specified procedures (which do
          not constitute an examination made in accordance with generally
          accepted auditing standards) that would not necessarily reveal matters
          of significance with respect to the comments set forth in this
          paragraph (iii), a reading of the minute books of the shareholders,
          the board of directors and any committees thereof of the Company and
          each of its consolidated subsidiaries, and inquiries of certain
          officials of the Company and its consolidated subsidiaries who have
          responsibility for financial and accounting matters, nothing came to
          their attention that caused them to believe that:

                    (A) the unaudited consolidated condensed financial
            statements of the Company and its consolidated subsidiaries included
            in the Registration Statement and the Prospectus do not comply in
            form in all material respects with the applicable accounting
            requirements of the Act, the Exchange Act and the related published
            rules and regulations thereunder, or are not in conformity with
            generally accepted accounting principles applied on a basis
            substantially consistent with that of the audited consolidated
            financial statements included in the Registration Statement and the
            Prospectus;

                    (B) at a specific date not more than five business days
            prior to the date of such letter, there were any changes in the
            capital stock or long-term debt of the Company and its consolidated
            subsidiaries or any decreases in net current assets or stockholders'
            equity of the Company and its consolidated subsidiaries, in each
            case compared with amounts shown on the June 30, 1999 unaudited
            consolidated condensed balance sheet included in the Registration
            Statement and the Prospectus, or for the period from July 1, 1999 to
            such specified date there were any decreases, as compared with the
            comparable period of 1998, in revenues, net income before income
            taxes or total or per share amounts of net income of the Company and
            its consolidated subsidiaries, except in all instances for changes,
            decreases or increases set forth in such letter; and

               (iv)  they have carried out certain specified procedures, not
          constituting an audit, with respect to certain amounts, percentages
          and financial information that are derived from the general accounting
          records of the Company and its consolidated subsidiaries and are
          included in the Registration Statement, the Prospectus and in the
          Company's Annual Report on Form 10-K and Quarterly Reports on Form 10-
          Q incorporated by reference in the Registration Statement and the
          Prospectus, and have compared such amounts, percentages and financial
          information with such records of the Company and its consolidated
          subsidiaries and with information derived from such records and have
          found them to be in agreement, excluding any questions of legal
          interpretation.

                                      -17-


    In the event that the letters referred to above set forth any such changes,
decreases or increases, it shall be a further condition to the obligations of
the Underwriters that (A) such letters shall be accompanied by a written
explanation of the Company as to the significance thereof, unless the
Representatives deem such explanation unnecessary, and (B) such changes,
decreases or increases do not, in the sole judgment of the Representatives, make
it impractical or inadvisable to proceed with the purchase and delivery of the
Securities as contemplated by the Registration Statement, as amended as of the
date hereof.

    References to the Registration Statement and the Prospectus in this
paragraph (d) with respect to either letter referred to above shall include any
amendment or supplement thereto at the date of such letter.

          (e) The Representatives shall have received from Ryder Scott Company,
     L.P., petroleum consultants, a letter or letters dated, respectively, the
     date hereof and the Firm Closing Date, in form and substance reasonably
     satisfactory to the Representatives, each stating, as of the date of such
     letter (or, with respect to matters involving changes or developments since
     the respective dates as of which specified information with respect to the
     oil and natural gas reserves is given in the Prospectus, as of the date not
     more than five days prior to the date of such letter), the conclusions and
     findings of such firm with respect to the oil and gas reserves of the
     Company.

          (f) The Representatives shall have received a certificate, dated the
     Firm Closing Date, of the principal executive officer and the principal
     financial or accounting officer of the Company to the effect that:

              (i)   the representations and warranties of the Company in this
          Agreement are true and correct as if made on and as of the Firm
          Closing Date; the Registration Statement, as amended as of the Firm
          Closing Date, does not include any untrue statement of a material fact
          or omit to state any material fact necessary to make the statements
          therein not misleading, and the Prospectus, as amended or supplemented
          as of the Firm Closing Date, does not include any untrue statement of
          a material fact or omit to state any material fact necessary in order
          to make the statements therein, in the light of the circumstances
          under which they were made, not misleading; and the Company has
          performed all covenants and agreements and satisfied all conditions on
          its part to be performed or satisfied at or prior to the Firm Closing
          Date;

              (ii)  no stop order suspending the effectiveness of the
          Registration Statement or any post-effective amendment thereto and no
          order directed at any document incorporated by reference in the
          Registration Statement or the Prospectus or any amendment or
          supplement thereto has been issued, and no proceedings for that
          purpose have been instituted or threatened or, to the best of the
          Company's knowledge, are contemplated by the Commission; and

              (iii) subsequent to the respective dates as of which information
          is given in the Registration Statement and the Prospectus, neither the
          Company nor any of its subsidiaries has sustained any material loss or
          interference with their respective businesses or properties from fire,
          flood, hurricane, accident or other calamity, whether or not covered
          by insurance, or from any labor dispute or any legal or governmental
          proceeding, and there has not been any material adverse change, or any
          development involving a prospective material adverse change, in the
          condition (financial or otherwise), management, business prospects,
          net

                                      -18-


          worth or results of operations of the Company or any of its
          subsidiaries, except in each case as described in or contemplated by
          the Prospectus.

          (g) The Representatives shall have received from each person who is a
     director or officer of the Company, Parker Drilling Company and the former
     shareholders of Hickman Drilling Company an agreement to the effect that
     such person will not, directly or indirectly, without the prior written
     consent of Prudential Securities Incorporated, on behalf of the
     Underwriters, offer, sell, offer to sell, contract to sell, pledge, grant
     any option to purchase or otherwise sell or dispose (or announce any offer,
     sale, offer of sale, contract of sale, pledge, grant of an option to
     purchase or other sale or disposition) of any shares of Common Stock or any
     securities convertible into, or exchangeable or exercisable for, shares of
     Common Stock for a period of 90 days after the date of this Agreement.

          (h) On or before the Firm Closing Date, the Representatives and
     counsel for the Underwriters shall have received such further certificates,
     documents or other information as they may have reasonably requested from
     the Company.

          (i) Prior to the commencement of the offering of the Securities, the
     Securities shall have been approved for listing on the New York Stock
     Exchange, subject to official notice of issuance.

    All opinions, certificates, letters and documents delivered pursuant to
this Agreement will comply with the provisions hereof only if they are
reasonably satisfactory in all material respects to the Representatives and
counsel for the Underwriters. The Company shall furnish to the Representatives
such conformed copies of such opinions, certificates, letters and documents in
such quantities as the Representatives and counsel for the Underwriters shall
reasonably request.

    The respective obligations of the several Underwriters to purchase and pay
for any Option Securities shall be subject, in their discretion, to each of the
foregoing conditions to purchase the Firm Securities, except that all references
to the Firm Securities and the Firm Closing Date shall be deemed to refer to
such Option Securities and the related Option Closing Date, respectively.

    8.   Indemnification and Contribution.
         --------------------------------

          (a) The Company agrees to indemnify and hold harmless each Underwriter
     and each person, if any, who controls any Underwriter within the meaning of
     Section 15 of the Act or Section 20 of the Exchange Act against any losses,
     claims, damages or liabilities, joint or several, to which such Underwriter
     or such controlling person may become subject under the Act, the Exchange
     Act or otherwise, insofar as such losses, claims, damages or liabilities
     (or actions in respect thereof) arise out of or are based upon:

               (i)  any untrue statement or alleged untrue statement made by the
          Company in Section 2 of this Agreement,

               (ii) any untrue statement or alleged untrue statement of any
          material fact contained in (A) the Registration Statement or any
          amendment thereto, any Preliminary Prospectus, the Prospectus or any
          amendment or supplement thereto or (B) any application or other
          document, or any amendment or supplement thereto, executed by the
          Company or based upon written information furnished by or on behalf of
          the Company filed in any

                                      -19-


          jurisdiction in order to qualify the Securities under the securities
          or blue sky laws thereof or filed with the Commission or any
          securities association or securities exchange (each an "Application")

               (iii)  the omission or alleged omission to state in the
          Registration Statement or any amendment thereto, any Preliminary
          Prospectus, the Prospectus or any amendment or supplement thereto, or
          any Application a material fact required to be stated therein or
          necessary to make the statements therein not misleading or

               (iv)   any untrue statement or alleged untrue statement of any
          material fact contained in any audio or visual materials provided by
          the Company or based upon written information furnished by or on
          behalf of the Company including, without limitation, slides, videos,
          films, tape recordings, used in connection with the marketing of the
          Securities, including, without limitation, statements communicated to
          securities analysts employed by the Underwriters;

     and will reimburse, as incurred, each Underwriter and each such controlling
     person for any legal or other expenses reasonably incurred by such
     Underwriter or such controlling person in connection with investigating,
     defending against or appearing as a third-party witness in connection with
     any such loss, claim, damage, liability or action; provided, however, that
                                                        --------  -------
     the Company will not be liable in any such case to the extent that any such
     loss, claim, damage or liability arises out of or is based upon any untrue
     statement or alleged untrue statement or omission or alleged omission made
     in such registration statement or any amendment thereto, any Preliminary
     Prospectus, the Prospectus or any amendment or supplement thereto, or any
     Application in reliance upon and in conformity with written information
     furnished to the Company by such Underwriter through the Representatives
     specifically for use therein; and provided, further, that the Company will
                                       --------  -------
     not be liable to any Underwriter or any person controlling such Underwriter
     with respect to any such untrue statement or omission made in any
     Preliminary Prospectus that is corrected in the Prospectus (or any
     amendment or supplement thereto) if the person asserting any such loss,
     claim, damage or liability purchased Securities from such Underwriter but
     was not sent or given a copy of the Prospectus (as amended or
     supplemented), other than the documents incorporated by reference therein,
     at or prior to the written confirmation of the sale of such Securities to
     such person in any case where such delivery of the Prospectus (as amended
     or supplemented) is required by the Act, unless such failure to deliver the
     Prospectus (as amended or supplemented) was a result of noncompliance by
     the Company with Section 5(d) and (a) of this Agreement.)  This indemnity
     agreement will be in addition to any liability which the Company may
     otherwise have.  The Company will not, without the prior written consent of
     the Underwriter or Underwriters purchasing, in the aggregate, more than
     fifty percent (50%) of the Securities, settle or compromise or consent to
     the entry of any judgment in any pending or threatened claim, action, suit
     or proceeding in respect of which indemnification may be sought hereunder
     (whether or not any such Underwriter or any person who controls any such
     Underwriter within the meaning of Section 15 of the Act or Section 20 of
     the Exchange Act is a party to such claim, action, suit or proceeding),
     unless such settlement, compromise or consent includes an unconditional
     release of all of the Underwriters and such controlling persons from all
     liability arising out of such claim, action, suit or proceeding.

          (b) Each Underwriter, severally and not jointly, will indemnify and
     hold harmless the Company, each of its directors, each of its officers who
     signed the Registration Statement and each person, if any, who controls the
     Company within the meaning of Section 15 of the Act or Section 20 of the
     Exchange Act against any losses, claims, damages or liabilities to which
     the Company or

                                      -20-


     any such director, officer or controlling person may become subject under
     the Act, the Exchange Act or otherwise, insofar as such losses, claims,
     damages or liabilities (or actions in respect thereof) arise out of or are
     based upon (i) any untrue statement or alleged untrue statement of any
     material fact contained in the Registration Statement or any amendment
     thereto, any Preliminary Prospectus, the Prospectus or any amendment or
     supplement thereto, or any Application or (ii) the omission or the alleged
     omission to state therein a material fact required to be stated in the
     Registration Statement or any amendment thereto, any Preliminary
     Prospectus, the Prospectus or any amendment or supplement thereto, or any
     Application or necessary to make the statements therein not misleading, in
     each case to the extent, but only to the extent, that such untrue statement
     or alleged untrue statement or omission or alleged omission was made in
     reliance upon and in conformity with written information furnished to the
     Company by such Underwriter through the Representatives specifically for
     use therein; and, subject to the limitation set forth immediately preceding
     this clause, will reimburse, as incurred, any legal or other expenses
     reasonably incurred by the Company or any such director, officer or
     controlling person in connection with investigating or defending any such
     loss, claim, damage, liability or any action in respect thereof. This
     indemnity agreement will be in addition to any liability which such
     Underwriter may otherwise have.

          (c) Promptly after receipt by an indemnified party under this Section
     8 of notice of the commencement of any action, such indemnified party will,
     if a claim in respect thereof is to be made against the indemnifying party
     under this Section 8, notify the indemnifying party of the commencement
     thereof; but the omission so to notify the indemnifying party will not
     relieve it from any liability which it may have to any indemnified party
     otherwise than under this Section 8. In case any such action is brought
     against any indemnified party, and it notifies the indemnifying party of
     the commencement thereof, the indemnifying party will be entitled to
     participate therein and, to the extent that it may wish, jointly with any
     other indemnifying party similarly notified, to assume the defense thereof,
     with counsel satisfactory to such indemnified party; provided, however,
                                                          --------  -------
     that if the defendants in any such action include both the indemnified
     party and the indemnifying party and the indemnified party shall have
     reasonably concluded that there may be one or more legal defenses available
     to it and/or other indemnified parties which are different from or
     additional to those available to the indemnifying party, the indemnifying
     party shall not have the right to direct the defense of such action on
     behalf of such indemnified party or parties and such indemnified party or
     parties shall have the right to select separate counsel to defend such
     action on behalf of such indemnified party or parties.  After notice from
     the indemnifying party to such indemnified party of its election so to
     assume the defense thereof and approval by such indemnified party of
     counsel appointed to defend such action, the indemnifying party will not be
     liable to such indemnified party under this Section 8 for any legal or
     other expenses, other than reasonable costs of investigation, subsequently
     incurred by such indemnified party in connection with the defense thereof,
     unless (i) the indemnified party shall have employed separate counsel in
     accordance with the proviso to the next preceding sentence (it being
     understood, however, that in connection with such action the indemnifying
     party shall not be liable for the expenses of more than one separate
     counsel (in addition to local counsel) in any one action or separate but
     substantially similar actions in the same jurisdiction arising out of the
     same general allegations or circumstances, designated by the
     Representatives in the case of paragraph (a) of this Section 8,
     representing the indemnified parties under such paragraph (a) who are
     parties to such action or actions) or (ii) the indemnifying party does not
     promptly retain counsel satisfactory to the indemnified party or (iii) the
     indemnifying party has authorized the employment of counsel for the
     indemnified party at the expense of the indemnifying party.  After such
     notice from the indemnifying party to such indemnified party, the
     indemnifying party will not be liable for the costs and expenses of any

                                      -21-


     settlement of such action effected by such indemnified party without the
     consent of the indemnifying party.

          (d) In circumstances in which the indemnity agreement provided for in
     the preceding paragraphs of this Section 8 is unavailable or insufficient,
     for any reason, to hold harmless an indemnified party in respect of any
     losses, claims, damages or liabilities (or actions in respect thereof),
     each indemnifying party, in order to provide for just and equitable
     contribution, shall contribute to the amount paid or payable by such
     indemnified party as a result of such losses, claims, damages or
     liabilities (or actions in respect thereof) in such proportion as is
     appropriate to reflect (i) the relative benefits received by the
     indemnifying party or parties on the one hand and the indemnified party on
     the other from the offering of the Securities or (ii) if the allocation
     provided by the foregoing clause (i) is not permitted by applicable law,
     not only such relative benefits but also the relative fault of the
     indemnifying party or parties on the one hand and the indemnified party on
     the other in connection with the statements or omissions or alleged
     statements or omissions that resulted in such losses, claims, damages or
     liabilities (or actions in respect thereof), as well as any other relevant
     equitable considerations.  The relative benefits received by the Company on
     the one hand and the Underwriters on the other shall be deemed to be in the
     same proportion as the total proceeds from the offering (before deducting
     expenses) received by the Company bear to the total underwriting discounts
     and commissions received by the Underwriters.  The relative fault of the
     parties shall be determined by reference to, among other things, whether
     the untrue or alleged untrue statement of a material fact or the omission
     or alleged omission to state a material fact relates to information
     supplied by the Company or the Underwriters, the parties' relative intent,
     knowledge, access to information and opportunity to correct or prevent such
     statement or omission, and any other equitable considerations appropriate
     in the circumstances.  The Company and the Underwriters agree that it would
     not be equitable if the amount of such contribution were determined by pro
     rata or per capita allocation (even if the Underwriters were treated as one
     entity for such purpose) or by any other method of allocation that does not
     take into account in the equitable considerations referred to above in this
     paragraph (d).  Notwithstanding any other provision of this paragraph (d),
     no Underwriter shall be obligated to make contributions hereunder that in
     the aggregate exceed the total public offering price of the Securities
     purchased by such Underwriter under this Agreement, less the aggregate
     amount of any damages that such Underwriter has otherwise been required to
     pay in respect of the same or any substantially similar claim, and no
     person guilty of fraudulent misrepresentation (within the meaning of
     Section 11(f) of the Act) shall be entitled to contribution from any person
     who was not guilty of such fraudulent misrepresentation.  The Underwriters'
     obligations to contribute hereunder are several in proportion to their
     respective underwriting obligations and not joint, and contributions among
     Underwriters shall be governed by the provisions of the Prudential
     Securities Incorporated Master Agreement Among Underwriters.  For purposes
     of this paragraph (d), each person, if any, who controls an Underwriter
     within the meaning of Section 15 of the Act or Section 20 of the Exchange
     Act shall have the same rights to contribution as such Underwriter, and
     each director of the Company, each officer of the Company who signed the
     Registration Statement and each person, if any, who controls the Company
     within the meaning of Section 15 of the Act or Section 20 of the Exchange
     Act, shall have the same rights to contribution as the Company.

    9.   Default of Underwriters.  If one or more Underwriters default in their
         -----------------------
obligations to purchase Firm Securities or Option Securities hereunder and the
aggregate number of such Securities that such defaulting Underwriter or
Underwriters agreed but failed to purchase is ten percent or less of the
aggregate number of Firm Securities or Option Securities to be purchased by all
of the Underwriters at such time hereunder, the other Underwriters may make
arrangements satisfactory to the Representatives for the

                                      -22-


purchase of such Securities by other persons (who may include one or more of the
non-defaulting Underwriters, including the Representatives), but if no such
arrangements are made by the Firm Closing Date or the related Option Closing
Date, as the case may be, the other Underwriters shall be obligated severally in
proportion to their respective commitments hereunder to purchase the Firm
Securities or Option Securities that such defaulting Underwriter or Underwriters
agreed but failed to purchase. If one or more Underwriters so default with
respect to an aggregate number of Securities that is more than ten percent of
the aggregate number of Firm Securities or Option Securities, as the case may
be, to be purchased by all of the Underwriters at such time hereunder, and if
arrangements satisfactory to the Representatives are not made within 36 hours
after such default for the purchase by other persons (who may include one or
more of the non-defaulting Underwriters, including the Representatives) of the
Securities with respect to which such default occurs, this Agreement will
terminate without liability on the part of any non-defaulting Underwriter or the
Company other than as provided in Section 10 hereof. In the event of any default
by one or more Underwriters as described in this Section 9, the Representatives
shall have the right to postpone the Firm Closing Date or the Option Closing
Date, as the case may be, established as provided in Section 3 hereof for not
more than seven business days in order that any necessary changes may be made in
the arrangements or documents for the purchase and delivery of the Firm
Securities or Option Securities, as the case may be. As used in this Agreement,
the term "Underwriter" includes any person substituted for an Underwriter under
this Section 9. Nothing herein shall relieve any defaulting Underwriter from
liability for its default.

    10.  Survival.  The respective representations, warranties, agreements,
         --------
covenants, indemnities and other statements of the Company, its officers and the
several Underwriters set forth in this Agreement or made by or on behalf of
them, respectively, pursuant to this Agreement shall remain in full force and
effect, regardless of (i) any investigation made by or on behalf of the Company,
any of its officers or directors, any Underwriter or any controlling person
referred to in Section 8 hereof and (ii) delivery of and payment for the
Securities.  The respective agreements, covenants, indemnities and other
statements set forth in Sections 6 and 8 hereof shall remain in full force and
effect, regardless of any termination or cancellation of this Agreement.

    11.  Termination. (a) This Agreement may be terminated with respect to the
         -----------
Firm Securities or any Option Securities in the sole discretion of the
Representatives by notice to the Company given prior to the Firm Closing Date or
the related Option Closing Date, respectively, in the event that the Company
shall have failed, refused or been unable to perform all obligations and satisfy
all conditions on its part to be performed or satisfied hereunder at or prior
thereto or, if at or prior to the Firm Closing Date or such Option Closing Date,
respectively,

               (i)  the Company or any of its subsidiaries shall have, in the
          sole judgment of the Representatives, sustained any material loss or
          interference with their respective businesses or properties from fire,
          flood, hurricane, accident or other calamity, whether or not covered
          by insurance, or from any labor dispute or any legal or governmental
          proceeding or there shall have been any material adverse change, or
          any development involving a prospective material adverse change
          (including without limitation a change in management or control of the
          Company), in the condition (financial or otherwise), business
          prospects, net worth or results of operations of the Company and its
          subsidiaries, except in each case as described in or contemplated by
          the Prospectus (exclusive of any amendment or supplement thereto);

               (ii) trading in the Common Stock shall have been suspended by the
          Commission or the New York Stock Exchange or trading in securities
          generally on the New York Stock Exchange or the Nasdaq National Market
          shall have been suspended or

                                      -23-


          minimum or maximum prices shall have been established on either such
          exchange or market system,

               (iii) a banking moratorium shall have been declared by New York
          or United States authorities; or

               (iv)  there shall have been (A) an outbreak or escalation of
          hostilities between the United States and any foreign power, (B) an
          outbreak or escalation of any other insurrection or armed conflict
          involving the United States or (C) any other calamity or crisis or
          material adverse change in general economic, political or financial
          conditions having an effect on the U. S. financial markets that, in
          the sole judgment of the Representatives, makes it impractical or
          inadvisable to proceed with the public offering or the delivery of the
          Securities as contemplated by the Registration Statement, as amended
          as of the date hereof.

         (b) Termination of this Agreement pursuant to this Section 11 shall be
     without liability of any party to any other party except as provided in
     Section 10 hereof.

    12.  Information Supplied by Underwriters.  The statements set forth in the
         ------------------------------------
last paragraph on the front cover page and under the heading "Underwriting" in
any Preliminary Prospectus or the Prospectus (to the extent such statements
relate to the Underwriters) constitute the only information furnished by any
Underwriter through the Representatives to the Company for the purposes of
Sections 2(b) and 8 hereof.  The Underwriters confirm that such statements (to
such extent) are correct.

    13.  Notices.  All communications hereunder shall be in writing and, if sent
         -------
to any of the Underwriters, shall be delivered or sent by mail, telex or
facsimile transmission and confirmed in writing to Prudential Securities
Incorporated, One New York Plaza, New York, New York 10292, Attention: Equity
Transactions Group; and if sent to the Company, shall be delivered or sent by
mail, telex or facsimile transmission and confirmed in writing to the Company at
Unit Corporation, 1000 Kensington Tower, 7130 South Lewis, Tulsa, Oklahoma
74136, attention:  Mark E. Schell.

    14.  Successors.  This Agreement shall inure to the benefit of and shall be
         ----------
binding upon the several Underwriters, the Company and their respective
successors and legal representatives, and nothing expressed or mentioned in this
Agreement is intended or shall be construed to give any other person any legal
or equitable right, remedy or claim under or in respect of this Agreement, or
any provisions herein contained, this Agreement and all conditions and
provisions hereof being intended to be and being for the sole and exclusive
benefit of such persons and for the benefit of no other person except that (i)
the indemnities of the Company contained in Section 8 of this Agreement shall
also be for the benefit of any person or persons who control any Underwriter
within the meaning of Section 15 of the Act or Section 20 of the Exchange Act
and (ii) the indemnities of the Underwriters contained in Section 8 of this
Agreement shall also be for the benefit of the directors of the Company, the
officers of the Company who have signed the Registration Statement and any
person or persons who control the Company within the meaning of Section 15 of
the Act or Section 20 of the Exchange Act.  No purchaser of Securities from any
Underwriter shall be deemed a successor because of such purchase.

    15.  Applicable Law.  The validity and interpretation of this Agreement, and
         --------------
the terms and conditions set forth herein, shall be governed by and construed in
accordance with the laws of the State of New York, without giving effect to any
provisions relating to conflicts of laws.

                                      -24-


    16.  Consent to Jurisdiction and Service of Process.  All judicial
         ----------------------------------------------
proceedings arising out of or relating to this Agreement may be brought in any
state or federal court of competent jurisdiction in the State of New York, and
by execution and delivery of this Agreement, the Company accepts for itself and
in connection with its properties, generally and unconditionally, the
nonexclusive jurisdiction of the aforesaid courts and waives any defense of
forum non conveniens and irrevocably agrees to be bound by any judgment rendered
thereby in connection with this Agreement.  A copy of any such process so served
shall be mailed by registered mail to the Company at its address provided in
Section 13 hereof; provided, however, that, unless otherwise provided by
                   --------  -------
applicable law, any failure to mail such copy shall not affect the validity of
service of such process.

    17.  Counterparts.  This Agreement may be executed in two or more
         ------------
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.

                                      -25-


    If the foregoing correctly sets forth our understanding, please indicate
your acceptance thereof in the space provided below for that purpose, whereupon
this letter shall constitute an agreement binding the Company and each of the
several Underwriters.

                          Very truly yours,

                          UNIT CORPORATION


                          By /s/ MARK E. SCHELL
                             ------------------------------------------
                                 Mark E. Schell
                                 General Counsel and Secretary

The foregoing Agreement is hereby
confirmed and accepted as of the
date first above written.

PRUDENTIAL SECURITIES INCORPORATED
CIBC WORLD MARKET CORP.
RAYMOND JAMES & ASSOCIATES, INC.

By PRUDENTIAL SECURITIES INCORPORATED



By /s/ JEAN-CLAUDE CANFIN
   --------------------------------------
   Jean-Claude Canfin
   Managing Director

For itself and on behalf of the Representatives.

                                      -26-


                                   SCHEDULE 1

                                  UNDERWRITERS

                                                              Number of Firm
                                                              Securities to
Underwriter                                                   be Purchased
- -----------                                                   -------------

Prudential Securities Incorporated.....................           2,394,000
CIBC World Markets Corp................................           1,512,000
Raymond James & Associates, Inc........................           1,134,000
Bear, Stearns & Co. Inc................................             140,000
Donaldson, Lufkin & Jenrette Securities Corporation....             140,000
A.G. Edwards & Sons, Inc...............................             140,000
Lehman Brothers Inc....................................             140,000
Merrill Lynch, Pierce, Fenner & Smith Incorporated.....             140,000
Morgan Stanley & Co. Incorporated......................             140,000
PaineWebber Incorporated...............................             140,000
Salomon Smith Barney Inc...............................             140,000
Robert W. Baird & Co. Incorporated.....................              70,000
Dain Rauscher Wessels..................................              70,000
Everen Securities, Inc.................................              70,000
First Albany Corporation...............................              70,000
First Union Capital Markets Corp.......................              70,000
Hanifen, Imhoff Inc....................................              70,000
Harris Webb & Garrison Inc.............................              70,000
Jefferies & Company, Inc...............................              70,000
Petrie Parkman & Co....................................              70,000
Southcoast Capital Corporation.........................              70,000
Sutro & Co. Incorporated...............................              70,000
Tucker Anthony Cleary Gull.............................              70,000
                                                              =============
Total..................................................           7,000,000

                                      -27-