1
 
                      INSTRUCTIONS AS TO USE OF MESA INC.
                           SUBSCRIPTION CERTIFICATES
 
                    CONSULT THE INFORMATION AGENT, YOUR BANK
                         OR BROKER AS TO ANY QUESTIONS
 
     The following instructions relate to a rights offering (the "Rights
Offering") by MESA Inc., a Texas corporation ("Mesa"), to the holders of its
Common Stock, par value $.01 per share ("Common Stock"), as described in Mesa's
Prospectus dated           , 1996, (the "Prospectus"). Holders of record of
Common Stock at the close of business on           , 1996 (the "Record Date")
are receiving .912 transferable subscription rights (the "Rights") for each
share of Common Stock held by them as of the close of business on the Record
Date. An aggregate of approximately 58,407,080 Rights exercisable to purchase an
aggregate of approximately 58,407,080 shares (the "Underlying Shares") of the
Series A 8% Cumulative Convertible Preferred Stock, par value $.01 per share, of
Mesa ("Series A Preferred Stock") are being distributed in connection with the
Rights Offering. Each Right is exercisable, upon payment of $2.26 in cash (the
"Subscription Price"), to purchase one share of Series A Preferred Stock (the
"Basic Subscription Privilege"). In addition, subject to the allocation
described below, each Right also carries the right to subscribe at the
Subscription Price for additional shares of Series A Preferred Stock available
as a result of unexercised Rights, if any (the "Oversubscription Privilege"), up
to the maximum amount offered by the Prospectus. Underlying Shares will be
available for purchase pursuant to the Oversubscription Privilege only to the
extent that all the Underlying Shares are not subscribed for through the
exercise of the Basic Subscription Privilege by the Expiration Date (as defined
below). If the Underlying Shares so available (the "Excess Shares") are not
sufficient to satisfy all subscriptions pursuant to the Oversubscription
Privilege, the available Excess Shares will be allocated pro rata (subject to
the elimination of fractional shares) among the holders of Rights who exercise
the Oversubscription Privilege, in proportion, not to the number of shares
requested pursuant to the Oversubscription Privilege, but to the number of
shares each beneficial holder has purchased pursuant to the Basic Subscription
Privilege; provided, however, that if such pro rata allocation results in any
holder being allocated a greater number of Excess Shares than such holder
subscribed for pursuant to the exercise of such holder's Oversubscription
Privilege, then such holder will be allocated only such number of Excess Shares
as such holder subscribed for and the remaining Excess Shares will be allocated
among all other holders exercising the Oversubscription Privilege. See "The
Rights Offering -- Subscription Privileges" in the Prospectus.
 
     No fractional Rights or cash in lieu thereof will be issued or paid. The
number of Rights distributed to each record holder has been rounded up the
nearest whole number in order to avoid issuing fractional Rights.
 
     The Rights will expire at 5:00 p.m., New York City time, on             ,
1996, unless extended by Mesa (as it may be extended, the "Expiration Date").
The Rights are expected to be traded on the New York Stock Exchange (the "NYSE")
until close of business on the last NYSE trading day preceding the Expiration
Date.
 
     The number of Rights to which you are entitled is printed on the face of
your Subscription Certificate. You should indicate your wishes with regard to
the exercise or transfer of your Rights by completing the appropriate form or
forms on the back of your Subscription Certificate and returning the
Subscription Certificate to the Subscription Agent in the envelope provided.
 
     YOUR SUBSCRIPTION CERTIFICATES MUST BE RECEIVED BY THE SUBSCRIPTION AGENT,
OR GUARANTEED DELIVERY REQUIREMENTS WITH RESPECT TO YOUR SUBSCRIPTION
CERTIFICATES MUST BE COMPLIED WITH, AND PAYMENT OF THE SUBSCRIPTION PRICE,
INCLUDING FINAL CLEARANCE OF ANY CHECKS, MUST BE RECEIVED BY THE SUBSCRIPTION
AGENT, ON OR BEFORE THE EXPIRATION DATE. ONCE A HOLDER OF RIGHTS HAS EXERCISED
THE BASIC SUBSCRIPTION PRIVILEGE AND/OR THE OVERSUBSCRIPTION PRIVILEGE, SUCH
EXERCISE MAY NOT BE REVOKED.
   2
 
1. SUBSCRIPTION PRIVILEGES.
 
     To exercise Rights, complete Section 1 of the Subscription Certificate and
send your properly completed and executed Subscription Certificate, together
with payment in full of the Subscription Price for each Underlying Share
subscribed for pursuant to the Basic Subscription Privilege and the
Oversubscription Privilege, to the Subscription Agent. All payments must be made
in United States dollars by (i) check or bank draft drawn upon a United States
bank or postal, telegraphic or express money order payable to "The American
Stock Transfer & Trust Company, as Subscription Agent"; or (ii) wire transfer of
funds to the account maintained by the Subscription Agent for such purpose at
          , Account No.           , ABA No.           ; or (iii) in the case of
persons acquiring Underlying Shares at an aggregate Subscription Price of $1.5
million or more, an Approved Payment Method as defined in the Prospectus.
Payments will be deemed to have been received by the Subscription Agent only
upon the (a) clearance of any uncertified check, (b) receipt by the Subscription
Agent of any certified check or bank draft drawn upon a United States bank or
postal, telegraphic or express money order, (c) the receipt of good funds in the
Subscription Agent's account designated above, or (d) receipt of funds by the
Subscription Agent through an Approved Payment Method. IF PAYING BY UNCERTIFIED
PERSONAL CHECK, PLEASE NOTE THAT THE FUNDS PAID THEREBY MAY TAKE AT LEAST FIVE
BUSINESS DAYS TO CLEAR. ACCORDINGLY, HOLDERS OF RIGHTS WHO WISH TO PAY THE
SUBSCRIPTION PRICE BY MEANS OF UNCERTIFIED PERSONAL CHECK ARE URGED TO MAKE
PAYMENT SUFFICIENTLY IN ADVANCE OF THE EXPIRATION DATE TO ENSURE THAT SUCH
PAYMENT IS RECEIVED AND CLEARS BY SUCH DATE, AND ARE URGED TO CONSIDER PAYMENT
BY MEANS OF CERTIFIED OR CASHIER'S CHECK, MONEY ORDER OR WIRE TRANSFER OF FUNDS.
You may also transfer your Subscription Certificate to your bank or broker in
accordance with the procedures specified in Instruction 3(a) below, make
arrangements for the delivery of funds on your behalf and request such bank or
broker to exercise the Rights represented by such Subscription Certificate on
your behalf. Alternatively, you may cause a written guarantee substantially in
the form available from the Subscription Agent (the "Notice of Guaranteed
Delivery") from a member firm of a registered national securities exchange or a
member of the National Association of Securities Dealers, Inc., a commercial
bank or trust company having an office or correspondent in the United States, or
a member in good standing of a recognized signature guarantee medallion program
(each of the foregoing being an "Eligible Institution"), to be received by the
Subscription Agent on or prior to the Expiration Date guaranteeing delivery of
your properly completed and executed Subscription Certificate within three NYSE
trading days following the date of the Notice of Guaranteed Delivery. If this
procedure is followed, your Subscription Certificates must be received by the
Subscription Agent within three NYSE trading days of the Notice of Guaranteed
Delivery. Additional copies of the Notice of Guaranteed Delivery may be obtained
upon request from the Subscription Agent at the address, or by calling the
telephone number, indicated below.
 
     Banks, brokers and other nominee holders of Rights who exercise the Basic
Subscription Privilege and the Oversubscription Privilege on behalf of
beneficial owners of Rights will be required to certify to the Subscription
Agent and Mesa (by delivery to the Subscription Agent of a Nominee Holder
Certification substantially in the form available from the Subscription Agent),
as to the aggregate number of Rights that have been exercised, and the number of
Underlying Shares that are being subscribed for pursuant to the Oversubscription
Privilege, by each beneficial owner of Rights (including such nominee itself) on
whose behalf such nominee holder is acting. In the event a Nominee Holder
Certification is not delivered in respect of a Subscription Certificate, the
Subscription Agent shall for all purposes (including for purposes of any
allocation in connection with the Oversubscription Privilege) be entitled to
assume that such certificate is exercised on behalf of a single beneficial
owner. If more Excess Shares are subscribed for pursuant to the Oversubscription
Privilege than are available for sale, Excess Shares will be allocated, as
described above, among beneficial owners exercising the Oversubscription
Privilege in proportion to such owners' exercise of Rights pursuant to the Basic
Subscription Privilege.
 
                                        2
   3
 
     The address and telecopier numbers of the Subscription Agent are as
follows:
 
If by Mail:
                                            If by Hand:
 
The American Stock Transfer                 The American Stock Transfer
& Trust Company                             & Trust Company
40 Wall Street, 46th Floor                  40 Wall Street, 46th Floor
New York, New York 10005                    New York, New York 10005
Attention: Corporate Stock Transfer Dept.   Attention: Corporate Stock Transfer
                                            Dept.
                       Telephone: (718) 921-8200
                       Facsimile: (718) 234-5001
 
                       If by Overnight Courier:
 
                       The American Stock Transfer
                       & Trust Company
                       40 Wall Street, 46th Floor
                       New York, New York 10005
                       Attention: Corporate Stock Transfer Dept.
 
     The address and telephone number of Morrow & Co., Inc., the Information
Agent, are as follows:
 
                       Morrow & Co., Inc.
                       909 Third Avenue
                       New York, New York 10002
                       (800) 566-9061 (toll free)
 
     If you exercise less than all of the Rights evidenced by your Subscription
Certificate by so indicating in Section 1 of your Subscription Certificate, the
Subscription Agent either (i) will issue to you a new Subscription Certificate
evidencing the unexercised Rights or (ii) if you so indicate in Section 2 of
your Subscription Certificate, will transfer the unexercised Rights in
accordance with your instructions. However, if you choose to have a new
Subscription Certificate sent to you or to a transferee, you or such transferee
may not receive any such new Subscription Certificate in sufficient time to
permit sale or exercise of the Rights evidenced thereby. If you have not
indicated the number of Rights being exercised, or if the dollar amount you have
forwarded is not sufficient (subject to the second sentence of Section 1 above)
to purchase (or exceeds the amount necessary to purchase) the number of shares
subscribed for, you will be deemed to have exercised the Basic Subscription
Privilege with respect to the maximum number of whole Rights which may be
exercised for the Subscription Price payment delivered by you, and, to the
extent that the Subscription Price payment delivered by you exceeds the product
of the Subscription Price multiplied by the number of Rights evidenced by the
Subscription Certificates delivered by you (such excess being the "Subscription
Excess"), you will be deemed to have exercised your Oversubscription Privilege
to purchase, to the extent available, that number of whole shares of Series A
Preferred Stock equal to the quotient obtained by dividing the Subscription
Excess by the Subscription Price.
 
2. DELIVERY OF STOCK CERTIFICATES, ETC.
 
     The following deliveries and payments will be made to the address shown on
the face of your Subscription Certificate unless you provide instructions to the
contrary in Section 1 of your Subscription Certificate.
 
          (a) Basic Subscription Privilege. As soon as practicable after the
     valid exercise of Rights and the Expiration Date, the Subscription Agent
     will mail to each exercising Rights holder certificates representing shares
     of Series A Preferred Stock purchased pursuant to the Basic Subscription
     Privilege.
 
          (b) Oversubscription Privilege. As soon as practicable after the
     Expiration Date and after all prorations and adjustments contemplated by
     the terms of the Rights Offering have been effected, the Subscription Agent
     will mail to each Rights holder who validly exercises the Oversubscription
     Privilege the number of shares allocated to such Rights holder pursuant to
     the Oversubscription Privilege. See "The Rights Offering -- Subscription
     Privileges -- Oversubscription Privilege" in the Prospectus.
 
                                        3
   4
 
          (c) Excess Payments. As soon as practicable after the Expiration Date
     and after all prorations and adjustments contemplated by the terms of the
     Rights Offering have been effected, the Subscription Agent will mail to
     each Rights holder who exercises the Oversubscription Privilege any excess
     funds received in payment of the Exercise Price for Excess Shares that are
     subscribed for by such Rights holder but not allocated to such Rights
     holder pursuant to the Oversubscription Privilege.
 
3. TO SELL OR TRANSFER RIGHTS.
 
     (a) Sale of Rights Through a Bank or Broker. To sell all Rights evidenced
by a Subscription Certificate through your bank or broker, so indicate in
Section 1 of your Subscription Certificate and deliver your properly completed
and executed Subscription Certificate to your bank or broker. If Section 1 of
your Subscription Certificate is completed without designating a transferee, the
Subscription Agent may thereafter treat the bearer of the Subscription
Certificate as the absolute owner of all of the Rights evidenced by such
Subscription Certificate for all purposes, and the Subscription Agent shall not
be affected by any notice to the contrary. Because your bank or broker cannot
issue Subscription Certificates, if you wish to sell less than all of the Rights
evidenced by a Subscription Certificate, either you or your bank or broker must
instruct the Subscription Agent as to the action to be taken with respect to the
Rights not sold, or you or your bank or broker must first have your Subscription
Certificate divided into Subscription Certificates of appropriate denominations
by following the procedures set forth in Instruction 4 below. The Subscription
Certificates evidencing the number of Rights you intend to sell can then be
transferred by your bank or broker in accordance with the instructions in this
Instruction 3(a).
 
     (b) Transfer of Rights to a Designated Transferee. To transfer all of your
Rights to a transferee other than a bank or broker, you must complete Section 2
of your Subscription Certificate in its entirety, execute the Subscription
Certificate and have your signature guaranteed by an Eligible Institution. A
Subscription Certificate that has been properly transferred in its entirety may
be exercised by a new holder without having a new Subscription Certificate
issued. In order to exercise, or otherwise take action with respect to, such a
transferred Subscription Certificate, the new holder should deliver the
Subscription Certificate, together with payment of the applicable Subscription
Price (with respect to the exercise of both the Basic Subscription Privilege and
the Oversubscription Privilege) and complete separate instructions signed by the
new holder, to the Subscription Agent in ample time to permit the Subscription
Agent to take the desired action. Because only the Subscription Agent can issue
Subscription Certificates, if you wish to transfer less than all of the Rights
evidenced by your Subscription Certificate to a designated transferee, you must
instruct the Subscription Agent as to the action to be taken with respect to the
Rights not sold or transferred, or you must divide your Subscription Certificate
into Subscription Certificates of appropriate smaller denominations by following
the procedures set forth in Instruction 4 below. The Subscription Certificate
evidencing the number of Rights you intend to transfer can then be transferred
by following the procedures set forth in this Instruction 3(b).
 
4. TO HAVE A SUBSCRIPTION CERTIFICATE DIVIDED INTO SMALLER DENOMINATIONS.
 
     To have a Subscription Certificate divided into smaller denominations, send
your Subscription Certificate, together with complete separate instructions
(including specification of the denominations into which you wish your Rights to
be divided) signed by you, to the Subscription Agent, allowing a sufficient
amount of time for new Subscription Certificates to be issued and returned so
that they can be used prior to the Expiration Date. Alternatively, you may ask a
bank or broker to effect such actions on your behalf. You signature must be
guaranteed by an Eligible Institution if any of the new Subscription
Certificates are to be issued in a name other than that in which the old
Subscription Certificate was issued. Subscription Certificates may not be
divided into fractional Rights, and any instruction to do so will be rejected.
As a result of delays in the mail, the time of the transmittal, the necessary
processing time and other factors, you or your transferee may not receive such
new Subscription Certificates in time to enable the Rights holder to complete a
sale or exercise by the Expiration Date. Neither Mesa nor the Subscription Agent
will be liable to either a transferor or transferee for any such delays.
 
                                        4
   5
 
5. EXECUTION.
 
     (a) Execution by Registered Holder. The signature on the Subscription
Certificate must correspond with the name of the registered holder exactly as it
appears on the face of the Subscription Certificate without any alteration or
change whatsoever. Persons who sign the Subscription Certificate in a
representative or other fiduciary capacity must indicate their capacity when
signing and, unless waived by the Subscription Agent in its sole and absolute
discretion, must present to the Subscription Agent satisfactory evidence of
their authority so to act.
 
     (b) Execution by Person Other than Registered Holder. If the Subscription
Certificate is executed by a person other than the holder named on the face of
the Subscription Certificate, proper evidence of authority of the person
executing the Subscription Certificate must accompany the same unless the
Subscription Agent, in its discretion, dispenses with proof of authority.
 
     (c) Signature Guarantees. Your signature must be guaranteed by an Eligible
Institution if you wish to transfer your Rights, as specified in Instruction
3(b) above, to a transferee other than a bank or broker, if you wish a new
Subscription Certificate or Certificates to be issued in a name other than that
in which the old Subscription Certificate was issued, as specified in
Instruction 4 above, or if you specify special payment or delivery instructions
pursuant to Section 2 of your Subscription Certificate.
 
6. METHOD OF DELIVERY.
 
     The method of delivery of Subscription Certificates and payment of the
Exercise Price to the Subscription Agent will be at the election and risk of the
Rights holder. If sent by mail, it is recommended that they be sent by
registered mail, properly insured, with return receipt requested, and that a
sufficient number of days be allowed to ensure delivery to the Subscription
Agent and the clearance of any checks sent in payment of the Exercise Price
prior to the Expiration Date.
 
7. SPECIAL PROVISIONS RELATING TO THE DELIVERY OF RIGHTS THROUGH DEPOSITORY
   FACILITY PARTICIPANTS.
 
     In the case of holders of Rights that are held of record through The
Depository Trust Company, Midwest Securities Trust Company, Philadelphia
Depository Trust Company or any other depository (each a "Depository"),
exercises of the Basic Subscription Privilege and the Oversubscription Privilege
may be effected by instructing the Depository to transfer Rights (such Rights,
"Depository Rights") from the Depository account of such holder to the
Depository account of the Subscription Agent, together with payment of the
Subscription Price for each Underlying Share subscribed for pursuant to the
Basic Subscription Privilege and the Oversubscription Privilege.
 
8. SUBSTITUTE FORM W-9.
 
     Each Rights holder who elects to exercise Rights must provide the
Subscription Agent with a correct Taxpayer Identification Number ("TIN") on
Substitute Form W-9, substantially in the form provided with these instructions.
A copy of Substitute Form W-9 may be obtained upon request from the Subscription
Agent at the address indicated above. Failure to provide the information on the
form may subject such holder to a $50.00 penalty and to 31% back-up federal
income tax withholding with respect to dividends that may be paid by Mesa on
shares of Series A Preferred Stock purchased upon the exercise of Rights and
payments that may be remitted to Rights holders by the Subscription Agent in
respect of Rights sold on such holders' behalf by the Subscription Agent.
 
                                        5