1
 
                                  [MESA LOGO]
                           1400 Williams Square West
                           5205 North O'Connor Blvd.
                            Irving, Texas 75039-3746
 
                                                                          , 1996
 
Dear Stockholder:
 
     You will find enclosed the Prospectus and other materials relating to the
rights offering by MESA Inc. ("Mesa").
 
     We request you to carefully review the Prospectus which describes how you
may participate in the rights offering. As indicated in the Prospectus, there is
a limited period of time, up to and including the Expiration Date, during which
you will be able to either purchase additional shares or sell your transferable
rights.
 
SUMMARY OF THE TERMS OF THE OFFERING
 
    - You will receive .912 transferable right for each share of Mesa Common
      Stock you owned on the Record Date (            , 1996)
 
    - You may purchase one share of Series A 8% Cumulative Convertible
      Preferred Stock for each right you receive at the Subscription Price of
      $2.26 per share.
 
    - Stockholders on the Record Date who have fully exercised the rights
      issued to them may subscribe for additional shares through the
      Oversubscription Privilege. If such oversubscriptions exceed the number of
      shares available, shares will be allocated to those stockholders who
      oversubscribe, based upon the number of shares such holders subscribed for
      pursuant to the basic subscription privilege, as more fully described in
      the Prospectus.
 
    - The rights offering expires on [            , 1996].
 
     If your shares are held in your name, a Subscription Certificate is
enclosed. If your shares are held in the name of your bank or broker, you must
contact your bank or broker if you wish to participate in this offering.
 
     The rights will trade on the New York Stock Exchange. Please decide if you
would like to (a) subscribe for additional shares, or (b) sell your rights.
Those stockholders who do not take any action will experience a dilution in the
value of their shares of Mesa Common Stock and a reduction in their
proportionate interest in Mesa.
 
     On behalf of the Board of Directors, we thank you for your support and
confidence and look forward to continuing to serve you.
 
                                     Sincerely,
 
                                     LOGO
                                     Chairman of the Board
 
     If you have any questions concerning the rights offering, please feel free
to contact the Information Agent for the rights offering, Morrow & Co. Inc., at
(800) 566-9061.