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                                                                   EXHIBIT 10.20



                       AMENDMENT TO EMPLOYMENT AGREEMENT


                 This Amendment to Employment Agreement (the "Amendment") is
entered into April 15, 1997 by and between COSTILLA ENERGY, INC. (the
"Company") and HENRY G. MUSSELMAN ("Musselman").

                                R E C I T A L S

                 A.       The Company and Musselman entered into an Employment
Agreement dated September 1, 1996, which Employment Agreement became effective
October 14, 1996 (the "Original Agreement").

                 B.       The Company and Musselman have agreed to modify the
Original Agreement by this Amendment for the sole purpose of modifying
Musselman's title under Section 3 of the Original Agreement.

                 NOW, THEREFORE, the Company and Musselman for good and
valuable consideration, the receipt and sufficiency of which are acknowledged
agree to modify the Original Agreement as follows:

                 1.       Section 3 of the Original Agreement is deleted and
replaced to read in its entirety as follows:

                 "Musselman's title during his term of employment shall be
                 Executive Vice President and Chief Operating Officer.  During
                 the term of this Agreement, and subject to the other
                 provisions of this Agreement, Musselman shall diligently
                 provide services to the Company."

                 2.       Except as modified by this Agreement, all other terms
of the Original Agreement shall remain unchanged.

                 EXECUTED the date and year first above written.

                                       COSTILLA ENERGY, INC.


                                       By: /s/ Michael J. Grella             
                                          -------------------------------
                                           Michael J. Grella, President


                                           /s/ Henry G. Musselman 
                                          -------------------------------
                                                HENRY G. MUSSELMAN