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                                                                    EXHIBIT 10.4


                 FIRST AMENDMENT TO THE STOCK PURCHASE AGREEMENT


         This First Amendment to the Stock Purchase Agreement (the "Amendment")
is made and entered into this 31st day of March, 2000, by and among Energy
Capital Investment Company PLC, an English investment company ("Energy PLC"),
EnCap Energy Capital Fund III-B, L.P., a Texas limited partnership ("EnCap
III-B"), BOCP Energy Partners, L.P., a Texas limited partnership ("BOCP"), EnCap
Energy Capital Fund III, L.P., a Texas limited partnership ("EnCap III"), Kayne
Anderson Energy Fund, L.P., a Delaware limited partnership ("Kayne"),
BancAmerica Capital Investors SBIC I, L.P., a Delaware limited partnership
("BACI"), Eos Partners, L.P., a Delaware limited partnership ("Eos Partners"),
Eos Partners SBIC, L.P., a Delaware limited partnership ("Eos SBIC"), Eos
Partners SBIC II, L.P., a Delaware limited partnership ("Eos SBIC II" and
together with Eos Partners and Eos SBIC, collectively referred to as "EOS"), and
SGC Partners II LLC, a Delaware limited liability company ("SGCP") (each
individually, an "Buyer" and collectively, the "Buyers") and Bargo Energy
Company, a Texas corporation (the "Company"), and evidences the following:

                                    RECITALS

         A. The Company and the Investors entered into a Stock Purchase
Agreement ("Agreement") on May 14, 1999, pursuant to which the Investors
purchased shares of Common Stock (as defined in the Agreement) and shares of
Preferred Stock (as defined in the Agreement) from the Company;

         B. The Company and the Investors have entered into a Subscription
Agreement dated even date herewith ("Subscription Agreement"), pursuant to which
the Investors have subscribed to purchase Units (as defined in the Subscription
Agreement);

         C. The parties to the Agreement desire to amend the Agreement as herein
provided to release all or a portion of the Investor's Common Stock which is
subject to certain provisions of the Agreement allowing repurchase of the shares
by the Company.

                                    AGREEMENT

         NOW, THEREFORE, for and in consideration of the foregoing Recitals and
mutual covenants contained herein, the sufficiency of which is hereby
acknowledged, the parties hereto, intending to be legally bound, do hereby agree
as follows:

         Section 1 AMENDMENT TO COMMON STOCK CLAW-BACK. The first sentence of
Article X of the Agreement shall be replaced with:



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         "In the event that, and only if, the Company, prior to the second
anniversary of the Closing Date, fully redeems all shares of Preferred Stock
issued to Buyers pursuant to this Agreement (the "Preferred Redemption"), then
the Company shall simultaneously purchase, and each Buyer shall sell, assign and
transfer, one-sixteenth (6.25%) of the total shares of Common Stock originally
issued to such Buyer pursuant to this Agreement plus any Other Securities,
subject to adjustment as provided herein, for a total purchase price of $100
(the "Redemption Price"); provided, however, if a Buyer purchases any Series C
Redeemable Preferred Stock pursuant to the Subscription Agreement, dated March
[ ], 2000, between the Buyer and the Company, the Company's right to purchase
Common Stock from such Buyer will terminate."

         Section 2 BINDING EFFECT. Each Investor and the Company by execution of
this Agreement shall be bound by and subject to the terms and obligations under
the Agreement, as amended by this Amendment.

         Section 3 NO OTHER CHANGES. Except as explicitly amended by the
Amendment, the terms, conditions, rights and obligations under the Agreement
shall remain in full force and effect.

         Section 4 COUNTERPARTS. This Amendment may be executed by the parties
hereto in any number of counterparts, each of which shall be deemed an original,
but all of which shall constitute one and the same agreement.




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         IN WITNESS WHEREOF, the Parties hereto have executed this Agreement as
of the date above first written.


ENERGY CAPITAL INVESTMENT COMPANY PLC



By:
   ------------------------------------------
   Gary R. Petersen
   Director

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



By:
   ------------------------------------------
   D. Martin Phillips
   Managing Director

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



By:
   ------------------------------------------
   D. Martin Phillips
   Managing Director

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



By:
   ------------------------------------------
   D. Martin Phillips
   Managing Director


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EOS PARTNERS, L.P.



By:
   ------------------------------------------
   Brian D. Young
   General Partner

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



By:
   ------------------------------------------
   Brian D. Young
   President

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:
   ------------------------------------------
   Brian D. Young
   President

SGC PARTNERS II LLC



By:
   ------------------------------------------
   V. Frank Pottow
   Managing Director



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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: Kayne Anderson Capital Advisors, L.P., its General Partner
    By: Kayne Anderson Investment Management, Inc., its General Partner



By:
   ------------------------------------------
   Daniel M. Weingeist
   Managing Director

BARGO ENERGY COMPANY



By:
   ------------------------------------------
   Jonathan M. Clarkson
   President