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                                                                    EXHIBIT 24.1

                              POWER OF ATTORNEY


     KNOW ALL MEN BY THESE PRESENTS, the undersigned, being certain of the
Officers and all of the Directors of Costilla Energy, Inc. (the "Company"), a
Delaware Corporation, do hereby constitute and appoint Cadell S. Liedtke,
Michael J. Grella and Bobby W. Page, or any one of them, with full power of
substitution, our true and lawful attorneys and agents, to do any and all acts
and things in our names in the capacities indicated which Cadell S. Liedtke,
Michael J. Grella and Bobby W. Page, or any one of them, may deem necessary or
advisable to enable the Company to comply with the Securities Exchange Act of
1934, as amended, and any rules, regulations and requirements of the
Securities and Exchange Commission in connection with the Company's Annual
Report on Form 10-K for the year ended December 31, 1996, including
specifically, but not limited to, the power and authority to sign such Form
10-K, any and all amendments thereto and any other forms or documents related
to such Form 10-K which are required under federal securities laws for us, or
any of us, in our names in the capacities indicated; and we do hereby ratify
and confirm all that Cadell S. Liedtke, Michael J. Grella and Bobby W. Page,
or any one of them, shall do or cause to be done by virtue hereof.  This Power
of Attorney may be signed in any number of counterparts, and each such
counterpart shall be considered an original hereof.

    IN WITNESS WHEREOF I have hereunto set my hand this 17th day of March,
1997.

                                             /s/ CADELL S. LIEDTKE
                                       -----------------------------------------
                                       CADELL S. LIEDTKE, Chairman of the Board,
                                       Chief Executive Officer and Director



                                              /s/ MICHAEL J. GRELLA
                                       -----------------------------------------
                                       MICHAEL J. GRELLA, President, Chief
                                       Operating Officer and Director


                                              /s/ HENRY G. MUSSELMAN
                                       -----------------------------------------
                                       HENRY G. MUSSELMAN, Executive Vice
                                       President and Director


                                                   /s/ BOBBY PAGE
                                       -----------------------------------------
                                       BOBBY W. PAGE, Senior Vice President,
                                       Treasurer and Chief Financial Officer


                                                 /s/ JERRY LANGDON
                                       -----------------------------------------
                                       JERRY LANGDON, Director


                                                 /s/ W. D. KENNEDY
                                       -----------------------------------------
                                       W. D. KENNEDY, Director