1
 
                                RIGHTS OFFERING
        FOR SHARES OF SERIES A 8% CUMULATIVE CONVERTIBLE PREFERRED STOCK
                                       OF
                                   MESA INC.
 
                                                                          , 1996
 
To Our Clients:
 
     We are enclosing for your consideration a Prospectus dated [July   , 1996]
describing the issuance to stockholders of record as of the close of business on
July 3, 1996 of transferable rights ("Rights") to purchase at the subscription
price shares of Series A 8% Cumulative Convertible Preferred Stock ("Series A
Preferred Stock") of MESA Inc. ("Mesa").
 
     Your attention is directed to the following:
 
     - Shareholders will receive .912 transferable Rights for each share of
       Common Stock of MESA Inc. held as of the close of business on the Record
       Date, July 3, 1996. No fractional rights or cash in lieu thereof will be
       paid, and the number of Rights distributed to each holder of Common Stock
       will be rounded up to the nearest whole number of Rights.
     
     - Rights will be admitted for trading on the New York Stock Exchange, the
       stock exchange on which Mesa's Common Stock is traded. Assuming a market
       exists, Rights may be purchased or sold through normal brokerage channels
       or sold through the Subscription Agent up to the last trading day prior
       to the Expiration Date, July 26, 1996, as more fully described in the
       Prospectus.
 
     - Basic Subscription Privilege: One Right will entitle the holder to
       purchase one share of Series A Preferred Stock of Mesa at the 
       subscription price of $2.26 per share.
 
     - Oversubscription Privilege: Any holder of Rights who fully exercises all
       Rights held by him is entitled to subscribe at the subscription price for
       shares that were not otherwise subscribed for during the basic
       subscription. However, if such oversubscriptions exceed the number of
       shares available, the shares available will be allocated among those who
       oversubscribed based on the number of shares subscribed for by such
       holder pursuant to the basic subscription privilege, as more fully 
       described in the Prospectus.
 
     - The expiration date of the rights offering is 5:00 p.m. New York City
       time, on July 26, 1996, unless extended by Mesa.
 
     Since we are the holder of record of the shares of Common Stock of Mesa
held in your Account, we have received your transferable Rights. We will
exercise or sell your Rights only in accordance with your instructions. If you
do not give us your instructions, your Rights will become valueless after the
Expiration Date.
 
     Please forward your instructions to us immediately by completing the form
on the reverse side. Your Rights will expire at 5:00 p.m. New York City time,
July 26, 1996, unless the rights offering is extended by MESA Inc.
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                             LETTER OF INSTRUCTIONS
 
To My Bank or Broker:
 
     The undersigned acknowledges receipt of the Prospectus relating to the
rights offering by MESA Inc. This letter instructs you to either exercise or
sell the Rights, as indicated below, which you hold for the account of the
undersigned upon the terms and conditions set forth in the Prospectus.
 
(1) BASIC SUBSCRIPTION PRIVILEGE
 
     - SELL           Rights (if no number is specified, all rights will be
       sold)
 
     - EXERCISE           Rights to purchase shares of Series A Preferred Stock
       of Mesa at the subscription price. (One Right is required for the
       purchase of each share of Series A Preferred Stock)
 
       I am enclosing a check for $          (equal to the number of shares to
       be purchased times the subscription price).
 
(2) OVERSUBSCRIPTION PRIVILEGE (available only to those who have fully exercised
    their Rights in the basic subscription privilege)
 
     - PURCHASE           shares of Series A Preferred Stock of Mesa at the
       subscription price, subject to availability as described in the
       Prospectus.
 
       I have enclosed a check for $          equal to the number of shares to
       be purchased pursuant to the oversubscription privilege times the
       subscription price. I understand that if I am not allocated the full
       amount of shares for which I have subscribed pursuant to the
       oversubscription privilege above, any excess payment will be refunded to
       me by you (without interest or deduction).
 
DATED:
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