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                            DNR-MESA HOLDINGS, L.P.
                          777 Main Street, Suite 2700
                            Fort Worth, Texas 76102


                                 April 6, 1997

Parker & Parsley  Petroleum Company
303 W. Wall, Suite 101
Midland, Texas  79701

Gentlemen:

         The undersigned serves as the sole general partner of DNR-MESA
Holdings, L.P. (the "Partnership"), and the Partnership is the owner of all
outstanding shares of the Series B 8% Cumulative Convertible Preferred Stock
(the "Series B Preferred Stock") of MESA, Inc. ("MXP"). This letter is provided
to you in connection with the execution and delivery of the Agreement and Plan
of Merger dated as of the date hereof (the "Merger Agreement"), among you, MXP,
Mesa Operating Co. and MXP Reincorporation Corp. Capitalized terms used herein
which are not otherwise defined have the meanings set forth in the Merger
Agreement.

         In consideration of the execution and delivery of the Merger Agreement
and the consummation of the Mergers and for other good and valuable
consideration, receipt of which is hereby acknowledged, the Partnership agrees
as follows:

         1. During the period commencing on the date hereof and ending on the
earlier of (i) the first anniversary of the date hereof, or (ii) the date of
abandonment of the Mergers and termination of the Merger Agreement pursuant to
Section 7.1 thereof (the "Lock-Up Period"), the Partnership will not offer,
sell, contract to sell or make any other distribution (collectively, a
"Transfer") of any shares of the Series B Preferred Stock or any securities of
RM Surviving Corporation received by the Partnership in exchange for shares of
the Series B Preferred Stock in connection with the Mergers (collectively,
"Securities"), except with your prior written consent (or after the Closing,
that of RM Surviving Corporation); provided that, the Partnership may Transfer
Securities to its partners at any time if prior to making such Transfer, the
Partnership receives the written agreement (which shall be for the benefit of
and enforceable by RM Surviving Corporation) of (i) each partner to enter into
an "Underwriting Lock-Up" (as defined in paragraph 2 below) with respect to the
Securities distributed to such partner under the circumstances set forth in
paragraph 2 hereof, and (ii) Richard E. Rainwater and each other partner which
is an Affiliate of Richard E. Rainwater (which for the purposes hereof includes
any trust established for the benefit of any member of his family), not to make
any Transfer of the Securities distributed to such partner during the remainder
of the Lock-Up Period.

         2. If within the 90 day period following the date of Closing of the
Mergers, RM Surviving Corporation shall file a registration statement with the
Securities and Exchange Commission pertaining to the issuance and sale of
common stock for its own account, the Partnership agrees that upon the written
request of RM Surviving Corporation and the managing 



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underwriter for such offering, the Partnership will enter into an agreement (an
"Underwriting Lock-Up") not to make Transfers of the Securities for such period
of time after the closing of such offering that RM Surviving Corporation deems
reasonably necessary (based upon the advice of such managing underwriter), but
in no event to be longer than a period of 180 days. The obligations arising
under this paragraph 2 are independent of those under paragraph 1.

         This letter agreement shall be governed by, and construed in
accordance with, the laws of the State of Texas applicable to contracts
executed in and to be performed in that State. The undersigned agrees that
irreparable damage would occur in the event that any provision of this letter
agreement was not performed in accordance with the terms hereof and that you
and RM Surviving Corporation shall be entitled to specific performance of the
terms hereof.

         This letter agreement and all obligations hereunder shall terminate if
the Mergers are abandoned and the Merger Agreement is terminated pursuant to
Section 7.1 thereof. The undersigned understands that you will rely upon the
representations set forth in this letter agreement in proceeding with the
Mergers. The undersigned confirms that this letter agreement is irrevocable and
shall be binding upon the undersigned's successors and assigns.



                                         Sincerely,

                                         DNR-MESA HOLDINGS, L.P

                                         By: Rainwater, Inc., general partner



                                         By:/s/ KENNETH A. HERSH
                                            ----------------------------------
                                            Kenneth A. Hersh, Vice President



Acknowledged and  Accepted

Parker & Parsley Petroleum Company



By: /s/ SCOTT D. SHEFFIELD
   --------------------------------
Name:   Scott D. Sheffield
     ------------------------------
Title:  President
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