1
                                                                       EXHIBIT 1


                                   [FORM OF]                          

                                   MESA, Inc.


                            Dealer Manager Agreement


                                                                    July 3, 1996

Lehman Brothers Inc.
Three World Financial Center
200 Vesey Street
New York, New York  10285

Ladies and Gentlemen:

                 The following will confirm our agreement relating to the
proposed rights offering (the "Rights Offering") to be undertaken by MESA,
Inc., a Texas corporation (the "Company"), pursuant to which the Company will
distribute to holders of record of its Common Stock, par value $.01 per share
(the "Common Stock"), transferable subscription rights (the "Rights") to
subscribe for an aggregate of 58,407,080 shares of its Series A 8% Cumulative
Convertible Preferred Stock, par value $.01 per share (the "Underlying
Shares"), at a subscription price of $2.26 per share in cash (the "Subscription
Price").

                  1.  The Rights Offering.  The Company proposes to undertake 
the Rights Offering pursuant to which each holder of Common Stock shall receive
 .912 of one Right for each share of Common Stock held of record at the close of
business on the date hereof.  Holders of Rights will be entitled to subscribe
for and purchase at the Subscription Price one share of Series A 8% Cumulative
Convertible Preferred Stock for each Right held, subject to reduction by the
Company under certain circumstances (the "Basic Subscription Privilege").  Any
holder of Common Stock who fully exercises all Rights issued to him is entitled
to subscribe for Shares which were not otherwise subscribed for by others on
primary subscription (the "Over-Subscription Privilege").  Shares acquired
pursuant to the Over-Subscription Privilege are subject to allotment, as more
fully discussed in the Prospectus (as defined herein).

                  2.  Appointment as Dealer-Manager.  The Company hereby
appoints you as sole Dealer-Manager and authorizes you to act as such in
connection with the Rights Offering.  As Dealer-Manager, you agree in
accordance with your customary practice to use your best efforts to solicit the
exercise of Rights and subscriptions for the Series A 8% Cumulative Convertible
Preferred Stock pursuant to the Rights Offering as further described in Section
6 hereof.

                  3.  No Liability for Acts of Brokers, Dealers, Banks and
Trust Companies.  You shall not be subject to any liability to the Company (or
any of the Company's affiliates) for any act or omission on the part of any
broker or dealer in securities (other than yourself) or any bank or trust
company or any other person, and you shall not be liable for your own acts or
omissions in performing your obligations as financial advisor or Dealer-Manager
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hereunder or otherwise in connection with the Rights Offering or the related
transactions, except for any losses, claims, damages, liabilities and expenses
determined in a final judgment by a court of competent jurisdiction to have
resulted directly from any such acts or omissions undertaken or omitted to be
taken by you through your gross negligence or willful misconduct.  In
soliciting or obtaining exercises of Rights, you, as Dealer-Manager, shall not
be deemed to be acting as the agent of the Company or as the agent of any
broker, dealer, bank or trust company, and no broker, dealer, bank or trust
company shall be deemed to be acting as your agent or as the agent of the
Company.

                  4.  The Offer Documents.  There will be used in connection 
with the Rights Offering certain materials in addition to the Registration
Statement, any Preliminary Prospectus or the Prospectus (each as defined
herein), including the Instructions as to the use of MESA, Inc. Subscription
Certificates; the proposed form of a letter to dealers, commercial banks, trust
companies and other nominees; the proposed form of a letter from dealers,
commercial banks, trust companies and other nominees to their customers
relating to the Rights Offering; and other soliciting materials relating to the
Rights Offering approved by the Company (collectively with the Registration
Statement, any Preliminary Prospectus and the Prospectus, the "Offer
Documents").  The Dealer Manager shall be given such opportunity to review and
comment upon the Offer Documents as is reasonable under the circumstances.

                 The Company agrees to furnish you with as many copies as you
may reasonably request of the final forms of the Offer Documents and you are
authorized to use copies of the Offer Documents in connection with your acting
as Dealer-Manager.  You hereby agree that you will not disseminate any written
material for or in connection with the solicitation of exercises of Rights
pursuant to the Rights Offering other than the Offer Documents.

                 The Company represents and agrees that no solicitation
material in addition to the Offer Documents and the documents to be filed
therewith as exhibits thereto (each in the form of which has been approved by
you) will be used in connection with the Rights Offering or filed with the
Commission (as defined herein) or any state or local governmental or regulatory
authority by or on behalf of the Company without your prior approval, which
approval will not be unreasonably withheld.  In the event that the Company uses
or permits the use of any such solicitation material in connection with the
Rights Offering or files any such solicitation material with the Commission or
any such state or local governmental or regulatory authority without your prior
approval, then you shall be entitled to withdraw as Dealer-Manager in
connection with the Rights Offering and the related transactions without any
liability or penalty to you or any other person identified in Section 12 as an
"indemnified party," and you shall be entitled to receive the payment of all
fees and expenses payable under this Agreement or the Engagement Letter (as
defined herein) which have accrued to the date of such withdrawal or which
otherwise thereafter become payable.

                 5.   Representations and Warranties.  The Company represents
and warrants to, and agrees with, the Dealer Manager that:
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                 (a)  A Registration Statement on Form S-3 (Registration No.
         333-03365) with respect to the Rights, the Underlying Shares and the
         Common Stock issuable upon conversion of the Underlying Shares (the
         "Conversion Shares") has (i) been prepared by the Company in
         conformity with the requirements of the Securities Act of 1933, as
         amended (the "Securities Act"), and the rules and regulations (the
         "Rules and Regulations") of the Securities and Exchange Commission
         (the "Commission") thereunder, (ii) been filed with the Commission
         under the Securities Act and (iii) become effective under the
         Securities Act.  Copies of such Registration Statement as amended to
         date have been delivered by the Company to you.  For purposes of this
         Agreement, "Effective Time" means the date and the time as of which
         such registration statement, or the most recent post-effective
         amendment thereto, if any, was declared effective by the Commission;
         "Effective Date" means the date of the Effective Time; "Preliminary
         Prospectus" means each prospectus included in such registration
         statement, or amendments thereof, before it becomes effective under
         the Securities Act and any prospectus filed with the Commission by the
         Company with the consent of the Dealer Manager pursuant to Rule 424(a)
         of the Rules and Regulations; "Registration Statement" means such
         Registration Statement, as amended at the Effective Time, including
         any documents incorporated by reference therein at such time; and
         "Prospectus" means such final prospectus, as first filed with the
         Commission pursuant to paragraph (1) or (4) of Rule 424(b) of the
         Rules and Regulations.  References made herein to any Preliminary
         Prospectus or the Prospectus shall be deemed to refer to and include
         the documents incorporated by reference therein pursuant to Item 12 of
         Form S-3 under the Securities Act as of the date of such Preliminary
         Prospectus or the Prospectus, as the case may be, and any reference to
         any amendment or supplement to any Preliminary Prospectus or the
         Prospectus shall be deemed to refer to and include any document filed
         under the Securities Exchange Act of 1934 (the "Exchange Act") after
         the date of such Preliminary Prospectus or the Prospectus, as the case
         may be, and incorporated by reference in such Preliminary Prospectus
         or the Prospectus, as the case may be; and any reference to any
         amendment to the Registration Statement shall be deemed to include any
         annual report of the Company filed with the Commission pursuant to
         Section 13(a) or 15(d) of the Exchange Act after the Effective Time
         that is incorporated by reference in the Registration Statement.  The
         Commission has not issued any order preventing or suspending the use
         of any Preliminary Prospectus or the Prospectus.

                 (b)  The Registration Statement conforms, and the Prospectus
         and any further amendments or supplements to the Registration
         Statement or the Prospectus will, when they become effective or are
         filed with the Commission, as the case may be, conform in all material
         respects to the requirements of the Securities Act and the Rules and
         Regulations and do not and will not, as of the applicable Effective
         Date (as to the Registration Statement and any amendment thereto) and
         as of the applicable filing date (as to the Prospectus and any
         amendment or supplement thereto) contain any untrue statement of a
         material fact or omit to state any material fact required to be stated
         therein or necessary to make the statements therein (with respect to
         the Prospectus, in the light of the circumstances under which they
         were made) not misleading; provided that no representation or warranty
         is made by the Company as to information
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         contained in or omitted from the Registration Statement or the
         Prospectus in reliance upon and in conformity with written information
         furnished to the Company by or on behalf of the Dealer Manager
         specifically for inclusion therein.

                 (c)  The documents incorporated by reference in the
         Prospectus, when they were filed with the Commission, conformed in all
         material respects to the requirements of the Exchange Act and the
         rules and regulations of the Commission thereunder, and none of such
         documents 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, in the light of the circumstances
         under which they were made, not misleading; and any further documents
         so filed and incorporated by reference in the Prospectus, when such
         documents are filed with Commission, will conform in all material
         respects to the requirements of the Exchange Act and the rules and
         regulations of the Commission thereunder and will not contain any
         untrue statement of a material fact or omit to state any material fact
         required to be stated therein or necessary to make the statements
         therein, in the light of the circumstances under which they were made,
         not misleading.

                 (d)  The Company and each of its subsidiaries (as defined in
         Section 18) have been duly incorporated and are validly existing as
         corporations in good standing under the laws of their respective
         jurisdictions of incorporation, are duly qualified to do business and
         are in good standing as foreign corporations in each jurisdiction in
         which their respective ownership or lease of property or the conduct
         of their respective businesses requires such qualification, and have
         all power and authority necessary to own or hold their respective
         properties and to conduct the businesses in which they are engaged,
         except where such power or authority would not have, singularly or in
         the aggregate, a material adverse effect on the Company and its
         subsidiaries taken as a whole.

                 (e)  The Rights to be issued and distributed by the Company
         have been duly and validly authorized and, when issued and delivered
         in accordance with the terms of the Offer Documents, will be duly and
         validly issued, and will constitute valid and legally binding
         obligations of the Company enforceable against the Company in
         accordance with their terms, no holder of the Rights is or will be
         subject to personal liability by reason of being such a holder, and
         the Rights conform to the description thereof contained in the
         Prospectus; the Underlying Shares have been duly and validly
         authorized and reserved for issuance upon exercise of the Rights and
         are free of statutory and contractual preemptive rights and are
         sufficient in number to meet the exercise requirements of the Rights
         Offering; and such Underlying Shares, when so issued and delivered
         against payment therefor in accordance with the terms of the Rights
         Offering, will be duly and validly issued, fully paid and
         non-assessable, with no personal liability attaching to the ownership
         thereof, and will conform to the description thereof contained in the
         Prospectus.

                 (f)  The Company has an authorized capitalization as set forth
         under the captions "Capitalization" and "Description of Capital Stock"
         in the Prospectus, and all
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         of the issued shares of capital stock of the Company have been duly
         and validly authorized and issued, are fully paid and non-assessable
         and conform to the description thereof contained under such captions
         in the Prospectus; all of the shares of Common Stock issuable upon
         conversion of the Underlying Shares have been duly and validly
         authorized and reserved for issuance upon such conversion and, when
         issued and delivered in accordance with the terms of the statement of
         resolution establishing the 8% Cumulative Convertible Preferred Stock
         (the "Statement of Resolution"), will be duly and validly issued,
         fully paid and nonassessable; and all of the issued shares of capital
         stock of each subsidiary of the Company have been duly and validly
         authorized and issued and are fully paid and non-assessable and
         (except for directors' qualifying shares and except as set forth in
         the Prospectus) are owned directly or indirectly by the Company, free
         and clear (except as otherwise set forth in the Prospectus) of all
         liens, encumbrances, equities or claims of any third party.

                 (g)  The execution, delivery and performance of this Agreement
         by the Company, the issuance of the Rights in accordance with the
         terms of the Offer Documents, the issuance of Underlying Shares in
         accordance with the terms of the Rights Offering and the issuance of
         Common Stock issuable upon conversion of the Underlying Shares in
         accordance with the terms of the Statement of Resolution, and the
         consummation by the Company of the transactions contemplated hereby,
         will not conflict with or result in a breach or violation of any of
         the terms or provisions of, or constitute a default under, any
         indenture, mortgage, deed of trust, loan agreement 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 is bound or
         to which any of the properties or assets of the Company or any of its
         subsidiaries is subject, nor will such actions result in any violation
         of the provisions of the charter or by-laws of the Company or any of
         its subsidiaries or any statute or any order, rule or regulation of
         any court or governmental agency or body having jurisdiction over the
         Company or any of its subsidiaries or any of their properties or
         assets; and except for the registration of the Rights, the Underlying
         Shares and the Common Stock issuable upon conversion of the Underlying
         Shares under the Securities Act and such consents, approvals,
         authorizations, registrations or qualifications as may be required
         under the Exchange Act and applicable state securities laws in
         connection with the distribution of the Rights and the sale of the
         Underlying Shares by the Company, no consent, approval, authorization
         or order of, or filing or registration with, any such court or
         governmental agency or body is required for the execution, delivery
         and performance of this Agreement by the Company and the consummation
         by it of the transactions contemplated hereby.

                 (h)  Other than certain rights of DNR-Mesa Holdings, L.P.
         ("DNR") under the Stock Purchase Agreement dated April 1, 1996 between
         DNR and the Company, as amended, (the "Stock Purchase Agreement") and
         as otherwise set forth in the Prospectus, there are no contracts,
         agreements or understandings between the Company and any person
         granting such person the right to require the Company to file a
         registration statement under the Securities Act with respect to any
         securities of the Company owned or to be owned by such person or to
         require the Company to include
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         such securities in the securities registered pursuant to the
         Registration Statement or in any securities being registered pursuant
         to any other registration statement filed by the Company under the
         Securities Act.

                 (i)  Neither the Company nor any of its subsidiaries has
         sustained, since the date of the latest audited financial statements
         included or incorporated by reference in the Prospectus, any material
         loss or interference with its business from fire, explosion, flood or
         other calamity, whether or not covered by insurance, or from any labor
         dispute or court or governmental action, order or decree; and, since
         such date, there has not been any change in the capital stock or
         long-term debt of the Company or any of its subsidiaries or any
         material adverse change, or any development involving a prospective
         material adverse change, in or affecting the general affairs,
         management, financial position, stockholders' equity or results of
         operations of the Company and its subsidiaries.

                 (j)  The financial statements (including the related notes and
         supporting schedules) filed as part of the Registration Statement or
         included or incorporated by reference in the Prospectus present fairly
         the consolidated financial position and results of operations of the
         entities purported to be shown thereby, at the dates and for the
         periods indicated, and have been prepared in conformity with generally
         accepted accounting principles applied on a consistent basis
         throughout the periods involved.

                 (k)  Arthur Andersen LLP, who have certified certain financial
         statements of the Company, whose report appears in the Prospectus or
         is incorporated by reference therein and who have delivered the letter
         referred to in Section 11(f) hereof, are independent public
         accountants as required by the Securities Act and the Rules and
         Regulations.

                 (l)  Except as described in the Prospectus, there are no legal
         or governmental proceedings pending to which the Company or any of its
         subsidiaries is a party or of which any property or asset of the
         Company or any of its subsidiaries is the subject which, if determined
         adversely to the Company or any of its subsidiaries, are reasonably
         likely to have a material adverse effect on the consolidated financial
         position, stockholders' equity, results of operations, business or
         prospects of the Company and its subsidiaries; and to the best of the
         Company's knowledge, except as disclosed in the Prospectus, no such
         proceedings are threatened or contemplated by governmental authorities
         or threatened by others.

                 (m)  The conditions for use of Form S-3, as set forth in the
         General Instructions thereto, have been satisfied.

                 (n)  There are no contracts or other documents which are
         required to be described in the Prospectus or filed as exhibits to the
         Registration Statement by the Securities Act or by the Rules and
         Regulations which have not been described in the Prospectus or filed
         as exhibits to the Registration Statement or incorporated therein by
         reference as permitted by the Rules and Regulations.
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                 (o)  Neither the Company nor any of its subsidiaries (i) is in
         violation of its charter or by-laws, (ii) is in default in any
         material respect, and no event has occurred which, with notice or
         lapse of time or both, would constitute such a default, in the due
         performance or observance of any term, covenant or condition contained
         in any material indenture, mortgage, deed of trust, loan agreement or
         other agreement or instrument to which it is a party or by which it is
         bound or to which any of its properties or assets is subject or (iii)
         is in violation in any material respect of any law, ordinance,
         governmental rule, regulation or court decree to which it or its
         properties or assets may be subject or has failed to obtain any
         material license, permit, certificate, franchise or other governmental
         authorization or permit necessary to the ownership of its properties
         or assets or to the conduct of its business, except any violation,
         default or failure to possess the same that would not have a material
         adverse effect on the Company and its subsidiaries taken as a whole.

                 (p)  This Agreement has been duly authorized, executed and
         delivered by the Company and, assuming the due authorization,
         execution and delivery by the Dealer Manager, constitutes the valid
         and legally binding agreement of the Company, enforceable against the
         Company in accordance with its terms, except as the enforceability
         thereof may be limited by bankruptcy, insolvency, reorganization,
         moratorium or similar laws relating to or affecting creditors' rights
         generally and by general principles of equity.

                 (q)  Prior to or on the date hereof, the Company and
         American Stock Transfer & Trust Company (the "Subscription Agent")
         will have entered into a subscription agency agreement (the
         "Subscription Agency Agreement") and the Company and Morrow & Co.,
         Inc. (the "Information Agent") will have entered into an information
         agency agreement (the "Information Agency Agreement"); when executed
         by the Company, each of the Subscription Agency Agreement and the
         Information Agency Agreement will have been duly authorized, executed
         and delivered by the Company and, assuming due authorization,
         execution and delivery by the Subscription Agent or the Information
         Agent, respectively, will constitute a valid and legally binding
         agreement of the Company enforceable in accordance with its terms,
         except as the enforceability thereof may be limited by bankruptcy,
         insolvency, reorganization, moratorium or similar laws relating to or
         affecting creditors' rights generally and by general principles of
         equity.

                 6.   Conduct by the Dealer Manager.  Subject to the terms
and conditions of this Agreement, the Dealer Manager agrees in accordance with
its customary practice to use its best efforts to solicit the exercise of the
Rights and subscriptions for Common Stock pursuant to the Offer Documents when
and as requested by the Company, and to respond to requests for information and
materials in connection with the Rights Offering.  Such services of the Dealer
Manager shall commence upon the commencement of the Rights Offering.

                 From time to time, the Dealer Manager may offer to the public
shares of Common Stock or 8% Cumulative Convertible Preferred Stock acquired by
it for its account  through the purchase and exercise of Rights or otherwise,
at such price or prices which, and
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at such time or times when, the Dealer Manager in its discretion may determine
in accordance with applicable laws, rules and regulations of the Commission,
whether or not prior to the expiration of the Rights Offering, and whether or
not for long or short account.  Any profits or losses realized upon such sales
shall be for the account of the Dealer Manager.

                 The Company hereby authorizes the Dealer Manager, or one or
more registered brokers chosen by the Dealer Manager, to act as the Company's
agent in making the Rights Offering to residents of such states as to which
such agent designation may be necessary to comply with applicable law.

                 7.   Compensation of Dealer Manager.  For acting as Dealer
Manager, the Company agrees to pay you, as compensation for your services as
Dealer Manager and for the services rendered and to be rendered by you as
financial advisor to the Company in connection with the Rights Offering and the
transactions related thereto, the fees described in the engagement letter dated
August 21, 1995 (the "Engagement Letter") between you and the Company, payable
in accordance with the terms of the Engagement Letter.  In addition, the
Company will reimburse certain of the Dealer Manager's expenses as set forth in
Section 8 hereof.

                 The Dealer Manager, from time to time, performs investment
banking and other financial services for the Company.  Other than the Dealer
Manager, the Company has not employed any brokers, dealers or underwriters in
connection with solicitation of exercise of Rights in the Rights Offering, and
except as described above, no other commissions, fees or discounts will be paid
in connection with the Rights Offering.

                 8.   Expenses.    The Company shall pay or cause to be paid (A)
all expenses (including any taxes) incurred in connection with the Rights
Offering and the preparation, issuance, execution, authentication and delivery
of the Rights and the Underlying Shares, (B) all fees and expenses (including,
without limitation, fees and expenses of the Company's accountants and counsel)
in connection with the preparation, printing, filing, delivery and shipping of
the Registration Statement (including the financial statements therein and all
amendments and exhibits thereto), each Preliminary Prospectus, the Prospectus,
the other Offer Documents and any amendments or supplements of the foregoing
and any documents incorporated by reference into any of the foregoing and any
printing, delivery and shipping of this Agreement, the costs of distributing
the terms of any agreement relating to any organization of soliciting dealers,
if any, to the members thereof by mail, telex or other means of communications,
and the preliminary and final forms of Blue Sky Memoranda, (C) all costs and
expenses of the Dealer Manager (including fees and expenses of counsel for the
Dealer Manager), (D) all filing fees and reasonable fees and disbursements of
counsel to the Dealer Manager incurred in connection with the qualification of
the distribution of the Rights and the offering and sale of the Underlying
Shares under state securities laws as provided for in Section 10(h) hereof, (E)
the filing fee of the National Association of Securities Dealers, Inc., (F) any
applicable listing or other fees, (G) the cost of printing certificates
representing the Rights and the Underlying Shares, (H) all advertising charges
pertaining to the Rights Offering, (I) all fees and expenses of the
Subscription Agent and the Information Agent, (J) the cost and charges of any
transfer agent or registrar and (K) all other costs and expenses
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incident to the performance of its obligations hereunder for which provision is
not otherwise made in this Section.  If the Rights Offering provided for herein
is not consummated by reason of acts of the Company pursuant to Section 13
hereof which prevent this Agreement from becoming effective, or by reason of
any failure, refusal or inability on the part of the Company to perform any
agreement on its part to be performed or because any other condition of the
Dealer Manager's obligations hereunder is not fulfilled (in each case other
than by reason of the Dealer Manager's gross negligence, willful misconduct or
failure, refusal or inability to perform its obligations hereunder), the
Company shall reimburse the Dealer Manager for all reasonable out-of-pocket
disbursements (including fees and disbursements of counsel) incurred by the
Dealer Manager in connection with any investigation or preparation made by it
in respect of Rights or the Underlying Shares or in contemplation of the
performance by it of its obligations hereunder.  All payments to be made by the
Company pursuant to this Section 8 shall be made promptly after the termination
or expiration of the Rights Offering or, if later, promptly after the related
fees, expenses or charges accrue and an invoice therefor is sent by you.  The
Company shall perform its obligations set forth in this Section 8 whether or
not the Rights Offering commences or any Rights are exercised pursuant to the
Rights Offering.

                 9.   Shareholder Lists; the Depository.  The Company will cause
you to be provided with any cards or lists showing the names and addresses of,
and the number of shares of Common Stock held by, the holders of shares of
Common Stock as of a recent date and will use its best efforts to cause you to
be advised from day to day during the period of the Rights Offering as to any
transfers of record of shares of Common Stock.

                 The Company will arrange for a bank or trust company
satisfactory to you and the Company to serve as Subscription Agent in
connection with the Rights Offering (the "Subscription Agent") and will arrange
for the Subscription Agent to advise you daily as to such matters as you may
reasonably request, including the number of Rights which have been exercised
pursuant to the Rights Offering.

                 10.  Covenants.  The Company covenants and agrees with the
Dealer Manager:

                 (a)  To use its best efforts to cause the Registration
         Statement and any amendments thereto to become effective; to advise
         the Dealer Manager, promptly after it receives notice thereof, of the
         time when the Registration Statement, or any amendment thereto,
         becomes effective or any supplement to the Prospectus or any amended
         Prospectus has been filed and to furnish the Dealer Manager with
         copies thereof; to prepare a Prospectus in a form approved by you and
         to file such Prospectus pursuant to Rule 424(b) under the Securities
         Act within the time prescribed by such rule; to advise the Dealer
         Manager, promptly after it receives notice thereof, of the issuance by
         the Commission of any stop order or of any order preventing or
         suspending the use of any Preliminary Prospectus or the Prospectus, of
         the suspension of the qualification of the Rights for offering or sale
         in any jurisdiction, of the initiation or threatening of any
         proceeding for any such purpose, or of any request by the Commission
         for the amending or supplementing of the Registration Statement or the
         Prospectus or for additional information; and, in the event of the
         issuance of any
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         stop order or of any order preventing or suspending the use of any
         Preliminary Prospectus or the Prospectus or suspending any such
         qualification, to use promptly its reasonable best efforts to obtain
         its withdrawal;

                 (b)  To deliver promptly to the Dealer Manager in New York
         City such number of the following documents as the Dealer Manager
         shall reasonably request:  (i) conformed copies of the Registration
         Statement as originally filed with the Commission and each amendment
         thereto (in each case excluding exhibits other than this Agreement,
         any other Offer Documents filed as exhibits, the computation of the
         ratio of earnings to fixed charges and the computation of per share
         earnings), (ii) each Preliminary Prospectus, the Prospectus and any
         amended or supplemented Prospectus and (iii) any document incorporated
         by reference in the Prospectus (excluding exhibits thereto); and, if
         the delivery of a prospectus is required at any time during which the
         Prospectus relating to the Rights or the Underlying Shares is required
         to be delivered under the Securities Act and if at such time any
         events shall have occurred 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 any material fact necessary in order to
         make the statements therein, in the light of the circumstances under
         which they were made when such Prospectus is delivered, not
         misleading, or, if for any other reason it shall be necessary during
         such period to amend or supplement the Prospectus or to file under the
         Exchange Act any document incorporated by reference in the Prospectus
         in order to comply with the Securities Act or the Exchange Act, to
         notify the Dealer Manager and, upon its request, to file such document
         and to prepare and furnish without charge to the Dealer Manager as
         many copies as the Dealer Manager may from time to time reasonably
         request of an amended or supplemented Prospectus which will correct
         such statement or omission or effect such compliance;

                 (c)  To file promptly with the Commission any amendment to the
         Registration Statement or the Prospectus or any supplement to the
         Prospectus that may, in the judgment of the Company or the Dealer
         Manager or its legal counsel, be necessary or advisable in connection
         with the distribution of the Rights or the sale of the Underlying
         Shares or be requested by the Commission;

                 (d)  Prior to filing with the Commission any (i) Preliminary
         Prospectus, (ii) amendment to the Registration Statement, any document
         incorporated by reference in the Prospectus or (iii) any Prospectus
         pursuant to Rule 424 of the Rules and Regulations, to furnish a copy
         thereof to the Dealer Manager and counsel for the Dealer Manager and
         obtain the consent of the Dealer Manager to the filing (which consent
         shall not be unreasonably withheld);

                 (e)  As soon as practicable after the Effective Date of the
         Registration Statement (it being understood that the Company shall
         have until at least 410 days after the end of the Company's current
         fiscal quarter), to make generally available to the Company's security
         holders and to deliver to the Dealer Manager a consolidated earnings
         statement of the Company and its subsidiaries (which need not be
         audited)
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                                                                              11



         complying with Section 11(a) of the Securities Act and the Rules and
         Regulations (including, at the option of the Company, Rule 158);

                 (f)  For a period of five years following the Effective Date
         of the Registration Statement, to furnish to the Dealer Manager copies
         of all materials furnished by the Company to its shareholders and all
         public reports and all reports and financial statements furnished by
         the Company to the principal national securities exchange upon which
         any of the Company's securities may be listed pursuant to requirements
         of or agreements with such exchange or to the Commission pursuant to
         the Exchange Act or any rule or regulation of the Commission
         thereunder;

                 (g)  Promptly from time to time to take such action as the
         Dealer Manager may reasonably request to qualify the Rights and the
         Underlying Shares for offering and sale under the securities laws of
         such jurisdictions as the Dealer Manager may request and to comply
         with such laws so as to permit the continuance of sales and dealings
         therein in such jurisdictions for as long as may be necessary to
         complete the distribution of the Rights and the Underlying Shares;
         provided that in connection therewith the Company shall not be
         required to qualify as a foreign corporation or to file a general
         consent to service of process in any jurisdiction;

                 (h)  Prior to the Effective Date of the Registration
         Statement, to apply for the listing of the Rights, the Underlying
         Shares and the Conversion Shares on the New York Stock Exchange, Inc.
         and to use its best efforts to complete that listing, subject only to
         official notice of issuance, prior to the expiration of the Rights
         Offering;

                 (i)  To take such steps as shall be necessary to ensure that
         neither the Company nor any subsidiary shall become an "investment
         company" within the meaning of such term under the Investment Company
         Act of 1940 and the rules and regulations of the Commission
         thereunder.

                 (j)  The Company shall advise the Dealer Manager, directly
         or through the Subscription Agent, daily of the number of Underlying
         Shares subscribed for, and arrange for the Subscription Agent to
         furnish the Dealer Manager with copies of written reports it furnishes
         to the Company concerning the Rights Offering;

                 (k)  The Company shall commence mailing the Offer Documents to
         record holders of the Common Stock not later than the second calendar 
         day following the record date for the Rights Offering, and complete 
         such mailing as soon as practicable; and

                 (l)  The Company shall reserve and keep available for issue 
         upon the exercise of the Rights such number of authorized but unissued
         shares of 8% Cumulative Convertible Preferred Stock as will be 
         sufficient to permit the exercise in full of all Rights issued, and
         shall reserve and keep available for issue upon the conversion of such
         Preferred Stock such number of authorized but unissued shares of
   12
                                                                              12



         Common Stock as will be sufficient to permit the conversion in full 
         of such Preferred Stock.

                 11.  Conditions of Dealer Manager's Obligations.  The
obligations of the Dealer Manager hereunder are subject to the accuracy, as of
the date hereof and at all times during the Rights Offering, of the
representations and warranties of the Company contained herein, to the
performance by the Company of its obligations hereunder and to the following
additional conditions:

                 (a)  The Registration Statement shall have become effective
         and the Prospectus shall have been timely filed with the Commission in
         accordance with Section 10(a); all post-effective amendments to the
         Registration Statement shall have become effective; no stop order
         suspending the effectiveness of the Registration Statement or any
         amendment or supplement thereto shall have been issued and no
         proceedings for the issuance of any such order shall have been
         initiated or threatened, and any request of the Commission for
         additional information (to be included in the Registration Statement
         or the Prospectus or otherwise) shall have been disclosed to you and
         complied with to your reasonable satisfaction.

                 (b)  The Dealer Manager shall not have been advised by the
         Company or shall have discovered and disclosed to the Company that the
         Registration Statement or the Prospectus or any amendment or
         supplement thereto, contains an untrue statement of fact which in your
         opinion, or in the opinion of counsel to the Dealer Manager, is
         material, or omits to state a fact which, in your opinion, or in the
         opinion of counsel to the Dealer Manager, is material and is required
         to be stated therein or is necessary to make the statements therein
         not misleading.

                 (c)  All corporate proceedings and other legal matters
         incident to the authorization, form and validity of this Agreement,
         the Rights, the Underlying Shares, the Statement of Resolution, the
         Common Stock issuable upon conversion of the Underlying Shares, the
         Registration Statement and the Prospectus, and all other legal matters
         relating to this Agreement and the transactions contemplated hereby
         shall be reasonably satisfactory in all material respects to counsel
         for the Dealer Manager, and the Company shall have furnished to such
         counsel all documents and information that they may reasonably request
         to enable them to pass upon such matters.

                 (d)  On or prior to the date hereof, you shall have received
         from Simpson Thacher & Bartlett, counsel for the Dealer Manager, such
         opinion or opinions with respect to corporate proceedings by the
         Company, the form of the Registration Statement and Prospectus (other
         than financial statements and other financial data), the validity of
         the Rights and the Underlying Shares, and other related matters as you
         may       reasonably request, and such counsel shall have received
         such documents and information as they may reasonably request to
         enable them to pass upon such matters.

                 (e)  On the date hereof there shall have been furnished to the
         Dealer Manager the signed opinion (addressed to the Dealer Manager) of
         Baker & Botts, L.L.P.,
   13
                                                                              13



         counsel for the Company, dated the date hereof and in form and
         substance satisfactory to counsel for the Dealer Manager, to the
         effect that:

                          (i)     The Company and each of its subsidiaries have
                 been duly incorporated and are validly existing as
                 corporations in good standing under the laws of their
                 respective jurisdictions of incorporation, and have all power
                 and authority necessary to own or hold their respective
                 properties and conduct the businesses in which they are
                 engaged;

                          (ii)    The Rights to be issued and distributed by
                 the Company have been duly and validly authorized and, when
                 issued and delivered against payment therefor in accordance
                 with the terms of the Offer Documents, will be duly and
                 validly issued, and will constitute valid and legally binding
                 obligations of the Company enforceable against the Company in
                 accordance with their terms, no holder of the Rights is or
                 will be subject to personal liability by reason of being such
                 a holder, and the Rights conform to the description thereof
                 contained in the Prospectus; the Underlying Shares have been
                 duly and validly authorized and reserved for issuance upon
                 exercise of the Rights and are free of statutory and
                 contractual preemptive rights and are sufficient in number to
                 meet the exercise requirements of the Rights Offering; and
                 such Underlying Shares, when so issued and delivered against
                 payment therefor in accordance with the terms of the Rights
                 Offering, will be duly and validly issued, fully paid and non-
                 assessable, with no personal liability attaching to the
                 ownership thereof, and will conform to the description thereof
                 contained under the caption "Description of Capital Stock" in
                 the Prospectus;

                          (iii)   The Company has an authorized capitalization
                 as set forth under the captions "Capitalization" and
                 "Description of Capital Stock" in the Prospectus, and all of
                 the issued shares of capital stock of the Company have been
                 duly and validly authorized and issued, are fully paid and
                 non- assessable and conform to the description thereof
                 contained under such captions in the Prospectus; all of the
                 shares of Common Stock issuable upon conversion of the
                 Underlying Shares have been duly and validly authorized and
                 reserved for issuance and, when issued and delivered in
                 accordance with the terms of the Rights Offering and the
                 Statement of Resolution, respectively, will be duly and
                 validly issued, fully paid and non-assessable; and all of the
                 issued shares of capital stock of Mesa Operating Co. have been
                 duly and validly authorized and issued and are fully paid,
                 non-assessable and (except for directors' qualifying shares
                 and except as set forth in the Prospectus) are owned directly
                 by the Company, free and clear of all liens, encumbrances,
                 equities or claims, other than as described in the Prospectus;

                          (iv)    There are no preemptive or other rights to
                 subscribe for or to purchase, nor any restriction upon the
                 voting or transfer of, any of the Underlying Shares or the
                 shares of Common Stock issuable upon conversion of
   14
                                                                              14



                 the Underlying Shares pursuant to the Company's charter or
                 by-laws or any agreement or other instrument known to such
                 counsel;

                               (v)  To the best of such counsel's knowledge,
                 there are no legal or governmental proceedings pending or
                 threatened to which the Company or any of its subsidiaries is
                 a party or of which any property or asset of the Company or
                 any of its subsidiaries is the subject which are required to
                 be disclosed in the Prospectus other than those dislcosed
                 therein;

                              (vi)  The Registration Statement was declared
                 effective under the Securities Act as of the date and time
                 specified in such opinion and no stop order suspending the
                 effectiveness of the Registration Statement has been issued
                 and, to the knowledge of such counsel, no proceeding for that
                 purpose is pending or threatened by the Commission;

                             (vii)  The Registration Statement, as of the
                 Effective Date, and the Prospectus, as of its date, and any
                 further amendments or supplements thereto, as of their
                 respective dates (other than the financial statements and
                 related schedules and other financial, reserve or statistical
                 information contained therein, as to which such counsel need
                 express no opinion) appeared on the face thereof to comply as
                 to form in all material respects with the requirements of the
                 Securities Act and the Rules and Regulations; the documents
                 incorporated by reference in the Prospectus (other than the
                 financial statements and related schedules and other
                 financial, reserve and statistical information contained
                 therein, as to which such counsel need express no opinion),
                 when they were filed with the Commission appeared on the face
                 thereof to comply as to form in all material respects with the
                 requirements of the Exchange Act and the rules and regulations
                 of the Commission thereunder;

                            (viii)  The statements contained in the Prospectus
                 under the caption "Description of Capital Stock," insofar as
                 they constitute a summary of the provisions of documents or
                 agreements referred to therein, constitute accurate summaries
                 of such provisions in all material respects;

                              (ix)  The statements contained in the Prospectus
                 under the caption "Certain Federal Income Tax Consequences,"
                 "Business -- Regulation and Prices," "Business -- Legal
                 Proceedings -- Preference unitholders," "-- Settlement with
                 WDB Group" and "-- Shareholder Litigation" insofar as they
                 represent statements or summaries of legal matters, are true
                 and correct;

                               (x)  To the best of such counsel's knowledge,
                 there are no contracts or other documents which are required
                 to be described in the Prospectus or filed as exhibits to the
                 Registration Statement by the Securities Act or by the Rules
                 and Regulations which have not been described or filed as
                 exhibits to the Registration Statement or incorporated therein
                 by reference as permitted by the Rules and Regulations;
   15
                                                                              15




                              (xi)  This Agreement has been duly authorized,
                 executed and delivered by the Company and constitutes the
                 valid and binding agreement of the Company, enforceable
                 against the Company in accordance with its terms, except as
                 enforcement may be affected by applicable bankruptcy,
                 insolvency, fraudulent transfer, reorganization, moratorium or
                 similar laws relating to or affecting the enforcement of
                 creditors' rights generally and by general principles of
                 equity (regardless of whether such enforceability is
                 considered in a proceeding in equity or law);

                             (xii)  The execution, delivery and performance of
                 this Agreement by the Company, the issuance of the Rights, the
                 issuance of the Underlying Shares and the issuance and
                 delivery of the Common Stock issuable upon conversion of the
                 Underlying Shares, will not conflict with or result in a
                 breach or violation of any of the terms or provisions of, or
                 constitute a default under, any indenture, mortgage, deed of
                 trust, loan agreement or other agreement or instrument known
                 to such counsel to which the Company or any of its
                 subsidiaries is a party or by which the Company or any of its
                 subsidiaries is bound or to which any of the properties or
                 assets of the Company or any of its subsidiaries is subject,
                 nor will such actions result in any violation of the
                 provisions of the charter or by-laws of the Company or any of
                 its subsidiaries or any statute or any order, rule or
                 regulation known to such counsel of any court or governmental
                 agency or body having jurisdiction over the Company or any of
                 its subsidiaries or any of their properties or assets; and,
                 except for the registration of the Rights, the Underlying
                 Shares and the Conversion Shares under the Securities Act and
                 such consents, approvals, authorizations, registrations or
                 qualifications as may be required under the Exchange Act and
                 applicable state securities laws in connection with the
                 distribution of the Rights and the issuance and sale of the
                 Underlying Shares, no consent, approval, authorization or
                 order of, or filing or registration with, any such court or
                 governmental agency or body is required for the execution,
                 delivery and performance of this Agreement by the Company and
                 the consummation by it of the transactions contemplated
                 hereby;

                            (xiii)  To the best of such counsel's knowledge,
                 other than certain rights of DNR under the Stock Purchase
                 Agreement and as otherwise set forth in the Prospectus, there
                 are no contracts, agreements or understandings between the
                 Company and any person granting such person the right (other
                 than rights which have been waived or satisfied) to require
                 the Company to file a registration statement under the
                 Securities Act with respect to any securities of the Company
                 owned or to be owned by such person or to require the Company
                 to include such securities in the securities registered
                 pursuant to the Registration Statement or in any securities
                 being registered pursuant to any other registration statement
                 filed by the Company under the Securities Act; and

                             (xiv)  Each of the Subscription Agency Agreement
                 and the Information Agency Agreement has been duly authorized,
                 executed and
   16
                                                                              16



                 delivered by the Company, and assuming due authorization,
                 execution and delivery by the Subscription Agent or the
                 Information Agent, as the case may be, each is a valid and
                 legally binding agreement of the Company enforceable in
                 accordance with its terms, except as the enforceability
                 thereof may be limited by bankruptcy, insolvency,
                 reorganization, moratorium or similar laws relating to or
                 affecting creditors' rights generally and by general
                 principles of equity;

         In rendering such opinion, such counsel may state that its opinion is
         limited to matters governed by the Federal laws of the United States
         of America and the laws of the State of Texas.  In giving the
         foregoing opinions, such counsel shall also state that they have
         participated in conferences with officers and other representatives of
         the Company and with representatives of the Company's independent
         public accountants at which conferences the contents of the
         Registration Statement and the Prospectus and related matters were
         discussed, and, although they have not independently verified and are
         not passing upon and assume no responsibility for the accuracy,
         completeness or fairness of the statements contained in the
         Registration Statement or the Prospectus except to the extent
         specified in paragraphs (ii), (iii), (viii) and (ix) above, no facts
         have come to the attention of such counsel which lead it to believe
         that (I) the Registration Statement, as of the Effective Date,
         contained any untrue statement of a material fact or omitted to state
         any material fact required to be stated therein or necessary in order
         to make the statements therein not misleading, or that the Prospectus,
         as of the date thereof or the date of such opinion, contained or
         contains any untrue statement of a material fact or omitted or omits
         to state any material fact required to be stated therein or necessary
         in order to make the statements therein, in the light of the
         circumstances under which they were made, not misleading (it being
         understood that such counsel need express no view with respect to the
         exhibits, financial statements and notes thereto, financial statement
         schedules and other reserve and statistical information included in
         the Registration Statement or the Prospectus) or (II) any document
         incorporated by reference in the Prospectus or any further amendment
         or supplement to any such incorporated document made by the Company,
         when they were filed with the Commission contained any untrue
         statement of a material fact or omitted 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.

                 (f)  Concurrently with the execution of this Agreement, the
         Company shall have furnished to the Dealer Manager a letter of Arthur
         Andersen LLP, addressed to the Dealer Manager and dated the date
         hereof (i) confirming that they are independent public accountants
         within the meaning of the Securities Act and are in compliance with
         the applicable requirements relating to the qualification of
         accountants under Rule 2-01 of Regulation S-X of the Commission, and
         (ii) stating, as of the date of the letter (or, with respect to
         matters involving changes or developments since the respective dates
         as of which specified financial information is given in the
         Prospectus, as of a date not more than five days prior to the date of
         the letter), the conclusions
   17
                                                                              17



         and findings of such firm with respect to the financial information
         and other matters specified by the Dealer Manager.

                 (g)  The Company shall have furnished to the Dealer Manager a
         certificate, dated the date hereof, of its Chairman of the Board, its
         President or a Vice President and its chief financial officer stating
         that:

                               (i)  To the best of their knowledge after
                 reasonable investigation, the representations, warranties and
                 agreements of the Company in Section 5 are true and correct as
                 of the date hereof; the Company has complied with all its
                 agreements contained herein; and the conditions set forth in
                 Sections 11(a) and 11(h) have been fulfilled; and

                              (ii)  They have carefully examined the
                 Registration Statement and the Prospectus and, in their
                 opinion (A) the Registration Statement and the Prospectus, as
                 of the Effective Date, did not include any untrue statement of
                 a material fact and did not omit to state any material fact
                 required to be stated therein or necessary to make the
                 statements therein not misleading, and (B) since the Effective
                 Date no event has occurred which should have been set forth in
                 a supplement or amendment to the Registration Statement or the
                 Prospectus.

                 (h)  (i)  Neither the Company nor any of its subsidiaries
         shall have sustained since the date of the latest audited financial
         statements included or incorporated by reference in the Prospectus any
         loss or interference with its business from fire, explosion, flood or
         other calamity, whether or not covered by insurance, or from any labor
         dispute or court or governmental action, order or decree, otherwise
         than as set forth or contemplated in the Prospectus or (ii) since such
         date there shall not have been any change in the capital stock or
         long-term debt of the Company or any of its subsidiaries or any
         change, or any development involving a prospective change, in or
         affecting the general affairs, management, financial position,
         stockholders' equity or results of operations of the Company and its
         subsidiaries, otherwise than as set forth or contemplated in the
         Prospectus, the effect of which, in any such case described in clause
         (i) or (ii), is, in the judgment of the Dealer Manager, so material
         and adverse as to make it impracticable or inadvisable to proceed with
         the Rights Offering.

                 (i)  Subsequent to the execution and delivery of this
         Agreement (i) no downgrading shall have occurred in the rating
         accorded the Company's debt securities by any "nationally recognized
         statistical rating organization", as that term is defined by the
         Commission for purposes of Rule 436(g)(2) of the Rules and Regulations
         and (ii) no such organization shall have publicly announced that it
         has under surveillance or review, with possible negative implications,
         its rating of any of the Company's debt securities.
   18
                                                                              18



                 (j)  The New York Stock Exchange, Inc. shall have approved the
         Rights, the Underlying Shares and the Conversion Shares for listing,
         subject only to official notice of issuance.

                 All opinions, letters, evidence and certificates mentioned
above or elsewhere in this Agreement shall be deemed to be in compliance with
the provisions hereof only if they are in form and substance reasonably
satisfactory to counsel for the Dealer Manager.  If any of the conditions
specified in this Section 11 shall not have been fulfilled when and as required
by this Agreement, this Agreement and all obligations of the Dealer Manager
hereunder may be canceled at, or at any time during the Rights Offering, by the
Dealer Manager.  Any such cancellation shall be without liability of the Dealer
Manager to the Company.  Notice of such cancellation shall be given the Company
in writing, or by telegraph or telephone and confirmed in writing.

                 12.  Indemnification and Contribution.  (a) The Company agrees
to hold harmless and indemnify you and your affiliates and any officer,
director, employee or agent of you or any such affiliates and any person
controlling (within the meaning of Section 20(a) of the Exchange Act) you or
any of such affiliates from and against any and all losses, claims, damages,
liabilities and expenses whatsoever, under the Securities Act or otherwise (as
incurred or suffered and including, but not limited to, any and all legal or
other expenses incurred in connection with investigating, preparing to defend
or defending any lawsuit, claim or other proceeding, commenced or threatened,
whether or not resulting in any liability, which legal or other expenses shall
be reimbursed by the Company promptly after receipt of any invoices therefor
from you), (A) arising out of or based upon (i) any untrue statement or alleged
untrue statement of a material fact contained in the Offer Documents or any
amendment or supplement thereto, in any other solicitation material used by the
Company or authorized by it for use in connection with the Rights Offering, or
in any blue sky application or other document prepared or executed by the
Company (or based on any written information furnished by the Company)
specifically for the purpose of qualifying any or all of the Rights under the
securities laws of any state or other jurisdiction (any such application,
document or information being hereinafter called a "Blue Sky Application") or
arising out of or based upon the omission or alleged omission to state in any
such document a material fact required to be stated therein or necessary in
order to make the statements therein, in the light of the circumstances under
which they were made, not misleading (other than statements or omissions made
in reliance upon and in conformity with information furnished by you in writing
to the Company expressly for use therein), (ii) any withdrawal or termination
by the Company of, or failure by the Company to make or consummate, the Rights
Offering, (iii) any actions taken or omitted to be taken by an indemnified
party with the consent of the Company or in conformity with actions taken or
omitted to be taken by the Company or (iv) any breach by the Company of any
representation or warranty, or any failure by the Company to comply with any
agreement or covenant, contained in this Agreement or (B) arising out of,
relating to or in connection with or alleged to arise out of, relate to or be
in connection with, the Rights Offering, any of the other transactions
contemplated thereby or the performance of your services as financial advisor
or Dealer-Manager with respect to the Rights Offering.  However, the Company
will not be obligated to indemnify an indemnified party for any loss, claim,
damage, liability or expense pursuant to clause (B) of the preceding sentence
which
   19
                                                                              19



has been determined in a final judgment by a court of competent jurisdiction to
have resulted directly from willful misconduct or gross negligence on the part
of such indemnified party.

                 (b)  The Dealer Manager shall indemnify and hold harmless
the Company, its officers and employees, each of its directors and each person,
if any, who controls the Company within the meaning of the Securities Act, from
and against any loss, claim, damage or liability, joint or several, or any
action in respect thereof, to which the Company or any such director, officer
or controlling person may become subject, under the Securities Act or
otherwise, insofar as such loss, claim, damage, liability or action arises out
of, or is based upon, (i) any untrue statement or alleged untrue statement of a
material fact contained (A) in any Offer Documents, or in any such amendment or
supplement, in any other solicitation material used by the Company or
authorized by it for use in connection with the Rights Offering or (B) in any
Blue Sky Application or (ii) the omission or alleged omission to state in any
Offer Documents, or in any such amendment or supplement, in any other
solicitation material used by the Company or authorized by it for use in
connection with the Rights Offering, or in any Blue Sky Application, any
material fact required to be stated therein or necessary to make the statements
therein not misleading, but in each case only to the extent that the untrue
statement or alleged untrue statement or omission or alleged omission was made
in reliance upon and in conformity with the written information furnished to
the Company by the Dealer Manager specifically for inclusion therein and
described in Section 16, and shall reimburse the Company and any such director,
officer or controlling person for any legal or other expenses reasonably
incurred by the Company or any such director, officer or controlling person in
connection with investigating or defending or preparing to defend against any
such loss, claim, damage, liability or action as such expenses are incurred.

                 (c)  If any lawsuit, claim or proceeding is brought against
any indemnified party in respect of which indemnification may be sought against
the indemnifying party pursuant to this Section 12, such indemnified party
shall promptly notify the indemnifying party of the commencement of such
lawsuit, claim or proceeding; provided, however, that the failure so to notify
the indemnifying party shall not relieve the indemnifying party from any
obligation or liability which it may have under this Section 12 except to the
extent that it has been prejudiced in any material respect by such failure and
in any event shall not relieve the indemnifying party from any other obligation
or liability which it may have to such indemnified party otherwise than under
this Section 12.  In case any such lawsuit, claim or proceeding shall be
brought against any indemnified party and such indemnified party shall notify
the indemnifying party of the commencement of such lawsuit, claim or
proceeding, the indemnifying party shall be entitled to participate in such
lawsuit, claim or proceeding, and, after written notice from the indemnifying
party to such indemnified party, to assume the defense of such lawsuit, claim
or proceeding with counsel of its choice at its expense; provided, however,
that such counsel shall be satisfactory to the indemnified party in the
exercise of its reasonable judgment.  Notwithstanding the election of the
indemnifying party to assume the defense of such lawsuit, claim or proceeding,
such indemnified party shall have the right to employ separate counsel and to
participate in the defense of such lawsuit, claim or proceeding, and the
indemnifying party shall bear the fees, costs and expenses of such separate
counsel (and shall pay such fees, costs and expenses promptly after receipt of
any invoice therefor from you) if (i) the use of counsel chosen by the
indemnifying party to
   20
                                                                              20



represent such indemnified party would present such counsel with a conflict of
interest; (ii) the defendants in, or targets of, any such lawsuit, claim or
proceeding include both an indemnified party and the indemnifying party, and
such indemnified party shall have reasonably concluded that there may be legal
defenses available to it or to other indemnified parties which are different
from or in addition to those available to the indemnifying party (in which case
the indemnfying party shall not have the right to direct the defense of such
action on behalf of the indemnified party); (iii) the indemnifying party shall
not have employed counsel satisfactory to such indemnified party, in the
exercise of such indemnified party's reasonable judgment, to represent such
indemnified party within a reasonable time after notice of the institution of
any such lawsuit, claim or proceeding; or (iv) the indemnifying party shall
authorize such indemnified party to employ separate counsel at the expense of
the indemnifying party.  The foregoing indemnification commitments shall apply
whether or not the indemnified party is a formal party to any such lawsuit,
claim or proceeding.  The indemnifying party shall not be liable for any
settlement of any lawsuit, claim or proceeding effected without its consent
(which consent will not be unreasonably withheld), but if settled with such
consent, the indemnifying party agrees, subject to the provisions of this
Section 12, to indemnify the indemnified party from and against any loss,
damage or liability by reason of such settlement.  The Company agrees to notify
you promptly, or cause you to be notified promptly, of the assertion of any
lawsuit, claim or proceeding against the Company, any of its officers or
directors or any person who controls any of the foregoing within the meaning of
Section 20(a) of the Exchange Act, arising out of or relating the Rights
Offering.  The Company further agrees that any settlement of a lawsuit, claim
or proceeding against it arising out of Rights Offering shall include an
explicit and unconditional release from the parties bringing such lawsuit,
claim or proceeding of the Dealer Manager, its affiliates, and any officer,
director, employee or agent of the Dealer Manager, and any person controlling
(within the meaning of Section 20(a) of the Exchange Act), which release shall
be reasonably satisfactory to you.

                 (d)  The Company and you agree that if any indemnification
sought by any indemnified party pursuant to this Section 12 is held by a court
to be unavailable for any reason, then (whether or not you are the indemnified
party) the Company, on the one hand, and you, on the other hand, shall
contribute to the losses, claims, damages, liabilities and expenses for which
such indemnification is held unavailable in such proportion as is appropriate
to reflect the relative benefits to the Company, on one hand, and you, on the
other hand, in connection with the matter giving rise to such losses, claims,
damages, liabilities and expenses, and other equitable considerations, subject
to the limitation that in any event your aggregate contribution to all losses,
claims, damages, liabilities and expenses with respect to which contribution is
available hereunder shall not exceed the amount of fees actually received by
you pursuant to this Agreement in connection with the Rights Offering.  It is
hereby agreed that the relative benefits to the Company, on the one hand, and
you, on the other hand, with respect to the Rights Offering and the other
transactions contemplated thereby shall be deemed to be in the same proportion
as (i) the total net proceeds from the offering of the Rights (before deducting
expenses) received by the Company, on the one hand, and the total fees received
from the Company by the Dealer Manager, on the other hand, bear to (ii) the
total gross proceeds from the offering of the Rights, in each case as set forth
in the Prospectus.
   21
                                                                              21




                 (e)  The amount paid or payable by an indemnified party as a
result of the losses, claims, damages, liabilities or expenses referred to in
the immediately preceding paragraph shall be deemed to include, subject to the
limitations set forth above, any legal or other expenses reasonably incurred by
such indemnified party in connection with investigating, preparing to defend or
defending any such action or claim.

                 (f)  The foregoing rights to indemnification and contribution
shall be in addition to any other rights which any indemnified parties may have
under common law or otherwise including, without limitation, rights to
indemnification, reimbursement and contribution under the Engagement Letter.

                 13.  Effective Date of Agreement; Termination.  This
Agreement shall become effective upon the later of the time on which the Dealer
Manager shall have received notification of the effectiveness of the
Registration Statement and the time which this Agreement shall have been
executed by all of the parties hereto.  At any time during the Rights Offering,
this Agreement may be terminated by you by giving notice as hereinafter
provided to the Company if (i) the Company shall have failed, refused or been
unable, at any applicable time during the Rights Offering, to perform any
agreement on its part to be performed hereunder, (ii) any other condition of
the Dealer Manager's obligations hereunder is not fulfilled, (iii) trading in
securities generally on the New York Stock Exchange or the American Stock
Exchange or in the over-the-counter market, or trading in any securities of the
Company on any exchange or in the over- the-counter market, shall have been
suspended or minimum prices shall have been established on any such exchanges
or such market by the Commission, by such exchange or by any other regulatory
body or governmental authority having jurisdiction, (iv) a banking moratorium
shall have been declared by Federal or state authorities, (v) the United States
shall have become engaged in hostilities, there shall have been an escalation
in hostilities involving the United States or there shall have been a
declaration of a national emergency or war by the United States or (vi) there
shall have occurred such a material adverse change in general economic,
political or financial conditions (or the effect of international conditions on
the financial markets in the United States shall be such) as to make it, in the
judgment of the Dealer Manager, inadvisable or impracticable to solicit
exercises of the Rights or perform any other of its obligations hereunder.  Any
termination of this Agreement pursuant to this Section 13 shall be without
liability on the part of the Company or the Dealer Manager, except as otherwise
provided in Sections 8 and 12 hereof.

                 Any notice referred to above may be given at the address
specified in Section 15 hereof in writing or by telegraph or telephone, and if
by telegraph or telephone, shall be immediately confirmed in writing.

                 14.  Survival of Certain Provisions.  The agreements contained
in Section 12 hereof and the representations, warranties and agreements of the
Company contained in Sections 5, 8 and 10 hereof shall survive the consummation
of or failure to commence the Rights Offering and shall remain in full force
and effect, regardless of any termination or cancellation of this Agreement or
any investigation made by or on behalf of any indemnified party.
   22
                                                                              22




                 15.  Notices.  Except as otherwise provided in the Agreement,
(a) whenever notice is required by the provisions of this Agreement to be given
to the Company, such notice shall be in writing or by telegraph addressed to
the Company at the address set forth in the Registration Statement, Attention:
Stephen K. Gardner, with a copy to: Carlos A. Fierro, Baker & Botts, L.L.P.,
2001 Ross Avenue, Suite 700, Dallas, TX 75201; and (b) whenever notice is
required by the provisions of this Agreement to be given to the Dealer Manager,
such notice shall be in writing or by telegraph addressed to Lehman Brothers
Inc., Three World Financial Center, 200 Vesey Street, New York, New York 10285,
Attention:  H.E. Lentz.

                 16.  Information Furnished by Dealer Manager.  The Dealer
Manager and the Company confirm that the statements set forth under the caption
"Prospectus Summary -- The Rights Offering    -- Dealer Manager" and under the
first two paragraphs under the caption "The Rights Offering -- The Dealer
Manager" on pages 11 and 32 in the Prospectus constitute the written
information furnished by or on behalf of the Dealer Manager referred to in
paragraph (b) of Section 5 hereof and in Section 12 hereof.

                 17.  Parties.  This Agreement shall inure to the benefit of
and be binding upon the Dealer Manager, the Company and their respective
successors.  This Agreement and the terms and provisions hereof are for the
sole benefit of only those persons, except that the representations,
warranties, indemnities and agreements of the Company contained in this
Agreement shall also be deemed to be for the benefit of the person or persons,
if any, who control the Dealer Manager within the meaning of Section 15 of the
Act.  Nothing in this Agreement shall be construed to give any person, other
than the persons referred to in this paragraph, any legal or equitable right,
remedy or claim under or in respect of this Agreement or any provision
contained herein.

                 18.  Definition of "Business Day" and "Subsidiary." For
purposes of this Agreement, (a) "Business Day" means any day on which the New
York Stock Exchange, Inc. is open for trading and (b) "Subsidiary" means a
subsidiary of the Company as defined in Rule 405 of the Rules and Regulations.

                 19.  Miscellaneous.  The invalidity or unenforceability of any
provisions of this Agreement shall not affect the validity or enforceability of
any other provisions of this Agreement, which shall remain in full force and
effect.  This Agreement may not be amended or modified except in writing signed
by each of the parties.

                 20.  Governing Law.  This Agreement shall be governed by and
construed in accordance with the laws of the State of New York.

                 21.  Counterparts.  This Agreement may be signed in one or
more counterparts, each of which shall constitute an original and all of which
together shall constitute one and the same agreement.
   23
                                                                              23



                 Please confirm, by signing and returning to us two
counterparts of this Agreement, that the foregoing correctly sets forth the
Agreement between the Company and you.



                                        Very truly yours,

                                        MESA, Inc.


                                        By:                            
                                            -----------------------------------




Confirmed and accepted as of
the date first above mentioned

LEHMAN BROTHERS INC.


By:
   ---------------------------------
   Authorized Representative