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                              BARGO ENERGY COMPANY

                               FIRST AMENDMENT TO
              SECOND AMENDED AND RESTATED SHAREHOLDERS' AGREEMENT

        This First Amendment ("Amendment") to the Second Amended and Restated
Shareholders' Agreement is effective for all purposes as of August 11, 1999, and
evidences the following:

        WHEREAS, B. Carl Price, Don Wm. Reynolds, Energy Capital Investment
Company PLC, an English investment company, EnCap Equity 1994 Limited
Partnership, a Texas limited partnership, BER Energy Resources, Ltd., a Texas
limited partnership (formerly Bargo Energy Resources, Ltd.), TJG Investments,
Inc., a Texas corporation, BEC Energy Company, a Texas general partnership
(formerly Bargo Energy Company), Tim J. Goff, Thomas Barrow, James E. Sowell,
BOC Operating Corporation, a Texas corporation (formerly Bargo Operating
Company, Inc.), EnCap Energy Capital Fund III-B, L.P., a Texas limited
partnership, BOCA Energy Partners, L.P., a Texas limited partnership, EnCap
Energy Fund III, L.P., a Texas limited partnership, Kayne Anderson Energy Fund,
L.P., a Delaware limited partnership, BancAmerica Capital Investors SBIC I,
L.P., a Delaware limited partnership, Eos Partners, L.P., a Delaware limited
partnership, Eos Partners SBIC, L.P., a Delaware limited partnership, Eos
Partners SBIC II, L.P., a Delaware limited partnership, and SGC Partners II LLC,
a Delaware limited partnership, entered into the Second Amended and Restated
Shareholders' Agreement, dated May 14, 1999 (the "Agreement");

        WHEREAS, the parties to the agreement desire to amend the agreement as
herein provided;

        NOW THEREFORE, the parties hereto, for good and valuable consideration,
intending to be legally bound, hereby agree as follows:

        Section 1. DEFINED TERMS. The terms capitalized herein have the meanings
given to them in the Agreement, unless otherwise defined herein.

        Section 2. BOARD OF DIRECTORS.

        (a) The first sentence of Section 2(a) is hereby replaced with the
following two sentences: "For so long as any of the Preferred Shares remain
outstanding: each of (i) EOS, (ii) Kayne and (iii) BACI (or the successor or
transferee of any such party), shall be entitled to name one (1) Designated
Nominee for Class III of the Company's Board of Directors; the Bargo Group
(including successors and transferees of its members) shall be entitled to name
two (2) Designated Nominees, and SGCP shall be entitled to name one (1)
Designated Nominee, for Class II of the Company's Board of Directors; and EnCap
(including successors and transferees of its members) shall be entitled to name
two (2) Designated Nominees for Class I of the Company's Board of Directors. In
addition, for so long as he is an employee of the Company, Jonathan M. Clarkson
shall be a Designated Nominee in Class I of the Company's Board of Directors."
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        (b) Section 2(b)(i) of the Agreement is amended to read in its entirety
as follows: "(i) to use its reasonable best efforts for so long as Jonathan M.
Clarkson is a Designated Nominee to cause Company's Board of Directors to be
composed of eight members and for so long as Mr. Clarkson is not a Designated
Nominee to cause the Company's Board of Directors to be composed of seven
members".

        Section 3. NO OTHER CHANGES. This amendment shall be incorporated into
and deemed part of the Agreement as if fully set forth therein. Except as
expressly set forth in this Amendment, all other terms and provisions of the
Agreement shall remain in full force and effect.

        IN WITNESS WHEREOF, this Amendment was executed as of the date above
first written.



                                BARGO ENERGY COMPANY


                                By:__________________________________
                                     Name:  Tim J. Goff
                                     Title: Chief Executive Officer


                                ENCAP EQUITY 1994 LIMITED PARTNERSHIP
                                By: EnCap Investments L.C., General Partner



                                By:__________________________________
                                     D. Martin Phillips
                                     Managing Director

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                                ENERGY CAPITAL INVESTMENT COMPANY PLC



                                By:__________________________________
                                     Gary R. Petersen
                                     Director


                                TJG INVESTMENTS, INC.



                                By:__________________________________
                                     Tim J. Goff
                                     President


                                BEC ENERGY COMPANY


                                By:__________________________________
                                     Tim J. Goff
                                     Manager


                                BER ENERGY RESOURCES, LTD.
                                By: BOC Operating Corporation
                                     General Partner


                                By:__________________________________
                                     Tim J. Goff
                                     President

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                                BOC OPERATING CORPORATION


                                By:__________________________________
                                     Tim J. Goff
                                     President


                                _____________________________________
                                Tim J. Goff

                                _____________________________________
                                Thomas Barrow

                                _____________________________________
                                James E. Sowell

                                _____________________________________
                                B. Carl Price

                                _____________________________________
                                Don Wm. Reynolds


                                ENCAP ENERGY CAPITAL FUND III, L.P.

                                By: EnCap Investments L.C., General Partner


                                By:__________________________________
                                     D. Martin Phillips
                                     Managing Director

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                                ENCAP ENERGY CAPITAL FUND III-B, L.P.
                                By: EnCap Investments L.C., General Partner


                                By:__________________________________
                                     D. Martin Phillips
                                     Managing Director


                                BOCP ENERGY PARTNERS, L.P.
                                By: EnCap Investments L.C., Manager


                                By:__________________________________
                                     D. Martin Phillips
                                     Managing Director


                                EOS PARTNERS, L.P.


                                By:__________________________________
                                     Name:___________________________
                                     Title:__________________________


                                EOS PARTNERS SBIC, L.P.
                                By: Eos SBIC General, L.P., its general
                                       partner
                                By: Eos SBIC, Inc., its general partner


                                By:__________________________________
                                     Name:___________________________
                                     Title:__________________________


                                EOS PARTNERS SBIC II, L.P.

                                By: Eos SBIC General II, L.P., its general
                                    partner

                                By: Eos SBIC II, Inc., its general partner


                                By:__________________________________
                                     Name:___________________________
                                     Title:__________________________

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                                SGC PARTNERS II LLC


                                By:___________________________________
                                     Name:____________________________
                                     Title:___________________________


                                BANCAMERICA CAPITAL INVESTORS SBIC I, L.P.

                                By: BancAmerica Capital Management
                                       SBIC I, LLC, its general partner

                                By: BancAmerica Capital Management I,
                                       L.P., its sole member

                                By: BACM I GP, LLC, its general partner


                                By:__________________________________
                                     J. Travis Hain
                                     Managing Director


                                KAYNE ANDERSON ENERGY FUND, L.P.


                                By:__________________________________
                                     Name:___________________________
                                     Title:__________________________

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