<PAGE>

                                                                    EXHIBIT 10.4

                     FIRST AMENDMENT TO EMPLOYMENT AGREEMENT

      This First Amendment to Employment Agreement (this "Amendment") is entered
into on November 9th, 2004, by and between Mission Resources Corporation, a
Delaware corporation (the "Company"), and Robert L. Cavnar (the "Executive").

                              W I T N E S S E T H:

      WHEREAS, the Company and the Executive are parties to an Employment
Agreement dated as of August 8, 2002, as amended to date, (the "Agreement"),
pursuant to which the Company employed the Executive as its Chairman, President
and Chief Executive Officer.

      WHEREAS, the Company and the Executive wish to amend the Agreement.

      NOW THEREFORE, in consideration of the promises and mutual covenants and
obligations herein set forth and for other good and valuable consideration, the
receipt, sufficiency and adequacy of which are hereby acknowledged, the parties
hereto hereby agree as follows, intending to be legally bound:

      1.    Capitalized terms used but not otherwise defined herein shall have
the meanings ascribed to such terms in the Agreement as defined therein unless
otherwise defined herein.

      2.    The second sentence of Section 5(g) of the Agreement is hereby
deleted and the following is substituted in place thereof:

      In the event that the excise tax relating to "parachute payments" under
      Section 280G of the Code applies to the Payment or any other payment by
      the Company to the Executive or other transaction entered into by the
      Executive pursuant to this Agreement or any other agreement, plan,
      instrument or obligation, in whatever form (collectively, the "Other
      Payments"), then the Company shall pay the Executive an additional payment
      in an amount such that, after payment of federal income taxes (but not the
      excise tax) on the Payment or any Other Payment, the Executive receives an
      additional amount equal to the excise tax originally imposed on the
      Payment or any Other Payment.

      3.    Except as amended by this Amendment, the Agreement shall remain in
full force and effect and is hereby ratified and affirmed. In the event of a
conflict between the terms in this Amendment and the Agreement, the Amendment
shall control.

      4.    This Amendment shall be construed in accordance with the laws of the
State of Texas.

      5.    In case of one or more of the provisions contained in this Amendment
for any reason shall be held to be invalid, illegal or unenforceable in any
respect, such invalidity, illegality or unenforceability shall not affect any
other provision of this Amendment, but this

<PAGE>

Amendment shall be construed as if such invalid, illegal or unenforceable
provisions had never been a part of this Amendment.

      6.    This Amendment shall be binding upon and inure to the benefit of the
Company, its successors, legal representatives and assigns and upon the
Executive, his or her heirs, executors, administrators, and representatives. Any
reference to the Company herein shall mean the Company as well as any successors
thereto.

      7.    This Amendment may be executed in any number of counterparts with
the same effect as if all signatories had signed the same document. All
counterparts must be construed together to constitute one and the same
instrument.

                            [Signature page follows]

                                       2

<PAGE>

      IN WITNESS WHEREOF, each of the parties hereto has executed this Amendment
as of the date and year first above written.

                                  COMPANY:

                                  MISSION RESOURCES CORPORATION

                                  By: /s/ Richard W. Piacenti
                                      ----------------------------------------
                                  Name: Richard W. Piacenti
                                  Title: Executive Vice President
                                         and Chief Financial Officer

                                  EXECUTIVE:

                                       /s/ Robert L. Cavnar
                                  --------------------------------------------
                                  Robert L. Cavnar

                                       3