Document:

<PAGE>   1
                                                                   EXHIBIT 10.5

                ASSIGNMENT, ACKNOWLEDGMENT, AGREEMENT AND WAIVER

         THIS Assignment, Acknowledgment, and Waiver (this "Agreement") dated
as of the 31st day of March, 2000, is among the persons listed as equity
investors on the signature pages hereof, (each an "Equity Investor" and
collectively the "Equity Investors"); BARGO ENERGY COMPANY, a Texas corporation
("Issuer") and CHASE BANK OF TEXAS, NATIONAL ASSOCIATION, as administrative
agent (in such capacity, the "Administrative Agent") for those Lenders
("Lenders") listed on Annex I attached hereto with Agent acting in such
capacity on behalf of such Lenders pursuant to the document also described on
Annex I (the Equity Investors, Issuer and Administrative Agent collectively
being hereinafter collectively called the "Parties"),

                              W I T N E S S E T H:

         WHEREAS, the Equity Investors have severally agreed pursuant to a
Subscription Agreement dated as of March 31, 2000, between the Issuer and each
Equity Investor (as the same may from time to time be amended, renewed,
supplemented or otherwise modified, the "Subscription Agreement") to purchase
shares of Preferred Stock and, at the election of the Equity Investor, Common
Stock or Warrants (collectively, the "Securities"), from the Issuer through
payment of the Equity Investor's share of the aggregate purchase price
("Purchase Price"), as set forth in the Subscription Agreement; and

         WHEREAS, in the Subscription Agreement the Equity Investors have
committed to purchase the Securities for an aggregate Purchase Price of
$22,500,000 and have the right and option to purchase up to an aggregate of
$45,000,000 of the Securities; and

         WHEREAS, Issuer has borrowed $22,500,000 from the Lenders under
Tranche A Term Loans (as defined in the Credit Agreement, dated as of March 31,
2000 among Issuer, Administrative Agent and the other lenders party thereto
("Credit Agreement")), evidenced by the Tranche A Term Notes (as defined in the
Credit Agreement); and

         WHEREAS, to induce the Lenders to make the Tranche A Term Loans,
Issuer has agreed to assign its rights under the Subscription Agreement to the
Administrative Agent on behalf of the Lenders, to enter into an escrow
arrangement ("Escrow") with the Administrative Agent and the Equity Investors
into which certificates and other documents representing the Securities, and
related agreements, shall be placed, with the Administrative Agent acting as
the escrow agent (in such capacity, the "Escrow Agent") as further described
below; and

         WHEREAS, the Equity Investors have agreed to acknowledge and agree to
the aforementioned assignment, to enter into the Escrow with the Issuer, the
Administrative Agent and the Escrow Agent in order to fund their subscription
pursuant to the Subscription Agreement and in order to carry out the intentions
of this Agreement; and

<PAGE>   2

         WHEREAS, the Equity Investors desire to waive any defenses they may
have against the Issuer with respect to the payment by them of their respective
Purchase Price other than satisfaction of the conditions to their respective
obligations set forth in Section 4.6 of the Subscription Agreement, and
recognize the Administrative Agent as a third-party beneficiary of the
Subscription Agreement;

         NOW, THEREFORE, in consideration of the premises and the agreements,
provisions and covenants herein contained, the Parties hereby agree as follows:

                                   SECTION  1
                      ASSIGNMENT OF SUBSCRIPTION AGREEMENT

         1.1      Assignment. Issuer, for good and valuable consideration, the
receipt of which is hereby acknowledged, hereby GRANTS, TRANSFERS and ASSIGNS
to the Agent for the benefit of the Lenders all of its rights, titles, and
interests in and to and arising from the Subscription Agreement, and any and
all other contracts or agreements, whether now or hereafter existing relating
to the purchase of the Securities by any Equity Investor, together with all
revenues, monies, proceeds, benefits, and payments due and to become due the
Issuer and accruing and to accrue unto the Issuer under and by virtue of the
Subscription Agreement, or any such other contract or agreement, and any and
all amendments and renewals thereof and supplements thereto.

                                    SECTION 2
              REPRESENTATIONS, WARRANTIES, AND COVENANTS OF ISSUER

         2.1      Representations and Warranties. The Issuer represents and
warrants, now and continuing throughout the term of this Agreement (which
representations and warranties will survive the delivery of this Agreement)
that:

                  (a)      the Issuer is the sole owner of its interests in the
                           Subscription Agreement;

                  (b)      the Subscription Agreement is valid and enforceable
                           and has not been altered, modified or amended in any
                           manner whatsoever save as herein set forth;

                  (c)      neither the Issuer nor the Equity Investors are in
                           default under any of the terms, covenants or
                           conditions thereof;

                  (d)      the Issuer's interest under the Subscription
                           Agreement is assignable pursuant to the terms
                           hereof; and

                  (e)      the Subscription Agreement commits the Equity
                           Investors to purchase Securities for an aggregate
                           Purchase Price of $22,500,000 and grants the

<PAGE>   3

                           Equity Investors the right and option to purchase
                           additional Securities for an aggregate Purchase
                           Price of $45,000,000.

         2.2      Covenants and Agreements of Issuer. The Issuer covenants and
                  agrees with the Administrative Agent:

                  (a)      to observe and perform all the obligations imposed
                           upon it under the Subscription Agreement and not to
                           do or permit to be done anything to impair the
                           security thereof;

                  (b)      not to execute any other assignment of its interests
                           in the Subscription Agreement;

                  (c)      not to alter, amend, modify or otherwise change the
                           terms of the Subscription Agreement without the prior
                           written consent of the Administrative Agent, or
                           cancel or terminate the Subscription Agreement or
                           accept a surrender thereof, or pledge, convey or
                           otherwise transfer or suffer or permit a pledge,
                           conveyance or other transfer of the Securities or of
                           any interest therein so as to effect directly or
                           indirectly, proximately or remotely, a cancellation,
                           termination or diminution of the obligations of the
                           Equity Investors thereunder;

                  (d)      to execute and deliver, and to require the Equity
                           Investors to execute and deliver, at the request of
                           the Administrative Agent, all such further
                           assurances, acknowledgments and certificates for the
                           purposes hereof as the Administrative Agent shall
                           from time to time require; and

                  (e)      that if the Issuer shall receive or become entitled
                           to receive any payments or other sums (whether paid
                           in cash or other property), distributions or payments
                           of any kind or description with respect to or on
                           account of the Subscription Agreement, to accept same
                           as agent for the Administrative Agent, to hold same
                           in trust for the Administrative Agent, and to
                           forthwith deliver same to the Administrative Agent in
                           the form received, with the endorsement of the Issuer
                           when necessary, to be applied by the Administrative
                           Agent pursuant to Section 6.

<PAGE>   4

                                    SECTION 3
          ACKNOWLEDGMENT, COVENANTS AND AGREEMENT OF EQUITY INVESTORS

         3.1      Acknowledgment. Each of the Equity Investors acknowledges the
assignment by the Issuer of its rights, titles, and interests in and to the
Subscription Agreement pursuant to Section 1 above.

         3.2      Covenants and Agreements of Equity Investors. Each Equity
Investor covenants and agrees with the Administrative Agent:

                  (a)      following receipt by Equity Investor of the Purchase
                           Notice (as defined in the Subscription Agreement) in
                           accordance with the Subscription Agreement and
                           provided (i) the Expiration Date (as defined in the
                           Subscription Agreement) has not occurred and (ii) the
                           conditions precedent to the Equity Investor's
                           obligations under the Subscription Agreement set
                           forth in Section 4.6 have been satisfied, to pay such
                           Equity Investor's Purchase Price as provided in the
                           Subscription Agreement into the Escrow with the
                           Escrow Agent on or before the Closing Date;

                  (b)      to observe and perform all the obligations imposed
                           upon it under its Subscription Agreement and not to
                           do or permit to be done anything to impair the
                           security thereof;

                  (c)      not to alter, amend, modify or otherwise change the
                           terms of the Subscription Agreement without the prior
                           written consent of the Administrative Agent, or
                           cancel or terminate the Subscription Agreement or
                           accept a surrender thereof, or pledge, convey or
                           otherwise transfer or suffer or permit a pledge,
                           conveyance or other transfer of its rights in and to
                           the Securities or any interest therein so as to
                           effect, directly or indirectly, proximately or
                           remotely, a cancellation, termination, or diminution
                           of the obligations of the Issuer thereunder; and

                  (d)      to execute and deliver at the request of the
                           Administrative Agent all such further assurances,
                           acknowledgments and certificates for the purposes
                           hereof as the Administrative Agent shall from time
                           to time reasonably require.

         3.3      Notices to Administrative Agent. Each Equity Investor
acknowledges that the Administrative Agent may act for and on behalf of the
Issuer under the Subscription Agreement. Upon receipt of a Purchase Notice,
each Equity Investor will cause copies of all notices or requests required or
permitted under the Subscription Agreement, including an Election to Receive
Warrants contemplated by Section 2.5 of the Subscription Agreement, to be
delivered to the Administrative Agent at the same time as such notices or
requests are delivered to the Issuer.

<PAGE>   5

                                    SECTION 4
                       AGREEMENTS OF ADMINISTRATIVE AGENT

         4.1      Withdrawal from Escrow; Delivery to Equity Investors. If,
prior to the Expiration Date, the Tranche A Equity Subscription Date (as
defined in the Credit Agreement) occurs and the Tranche A Loan has not been
repaid in full, the Administrative Agent may, and, at the request of the
Company shall, deliver a certificate executed by an officer of the
Administrative Agent to the Escrow Agent as contemplated by Section 4(a) of the
Escrow Agreement stating that the Tranche A Equity Subscription Date has
occurred and that amounts remain outstanding on the Tranche A Loan, and
withdraw from Escrow the Purchase Notices. The Administrative Agent shall
complete the blanks in the Purchase Notice by filling in the aggregate Purchase
Price, the Total Number of Units, the Investor's Share of Units, the number of
shares of Common Stock to be purchased by the Equity Investor, the Closing Date
and the wire transfer instructions for payment of the Purchase Price, all in
accordance with the terms of the Subscription Agreement. The Administrative
Agent shall promptly deliver a Purchase Notice to each Equity Investor as
provided in the Subscription Agreement. Notwithstanding anything set forth
herein, no Equity Investor shall have an obligation to purchase Units if the
Purchase Notice is not delivered to the Equity Investor prior to the Expiration
Date, as defined in the Subscription Agreement.

         4.2      Actions on the Closing Date. On the Closing Date (as defined
in the Subscription Agreement), the Administrative Agent shall deliver a
certificate executed by an officer of the Administrative Agent setting for the
number of shares of Preferred Stock and Common Stock or Warrants (based on
copies of the Election to Receive Warrants received by the Administrative
Agent) being purchased by each Equity Investor, and directing the Escrow Agent
to deliver such securities to the Equity Investor upon receipt of the Purchase
Price payable by the Equity Investor.

         4.3      Release. Upon the earlier of payment in full of the Tranche A
Term Loan or if Purchase Notices have not been delivered to the Equity
Investors, the Expiration Date (as defined in the Subscription Agreement), the
Administrative Agent shall withdraw the Escrowed Items from the Escrow and
promptly return them to the Issuer, and shall assign any rights it may have
under the Subscription Agreement to the Issuer.

                                   SECTION 5
                                     ESCROW

         5.1      Escrow Agreement. The parties hereto agree to enter into the
Escrow Agreement in the form thereof attached hereto as Exhibit A.

         5.2      Escrow Items. Issuer has placed into Escrow and delivered to
the Escrow Agent the Escrow Items (other than the Purchase Price) as defined in
the Escrow Agreement.

         5.3      No Retention. The holding of the Preferred Stock by the
Escrow Agent pursuant to the Escrow Agreement shall not be deemed a retention
by the Administrative Agent or the Lenders in satisfaction of the Indebtedness.

<PAGE>   6

                                    SECTION 6
                                PAYMENT ON NOTES

         6.1      Payments. The Agent hereby agrees that upon receipt of the
Purchase Price for Securities from the Escrow Agent, the Agent will apply such
funds toward repayment of the Tranche A Term Loan Notes corresponding to such
Purchase Price (and the Tranche B Term Loan Notes, under the circumstances
provided in Section 2.4 of the Subscription Agreement).

                                    SECTION 7
                RIGHTS, DUTIES AND POWERS OF ADMINISTRATIVE AGENT

         7.1      Rights and Powers. The Issuer does hereby irrevocably
authorize and empower the Administrative Agent to do the following, by and on
behalf of the Issuer, in the Issuer's name, place and stead: (a) demand,
receipt for and receive all sums of money to which this Agreement relates; (b)
commence, maintain or discontinue any action, suit or other proceeding which it
deems advisable to collect or enforce the payment of the sums, monies,
benefits, revenues, proceeds and payments assigned hereby; (c) to endorse in
the name of the Issuer any checks, drafts or other instruments payable to the
Issuer or to its order, as may be issued in whole or in partial payment in
connection with the Subscription Agreement; (d) to deliver the Purchase Notice,
Preferred Stock Certificates and Warrants to the Equity Investors, to receive
the Purchase Price from the Equity Investors, to deliver the Transfer Agent
Instructions to the Issuer's transfer agent and to otherwise take such actions
as the Administrative Agent shall deem appropriate hereunder and under the
Subscription Agreement to deliver the Securities in exchange for the Purchase
Price; and (e) to fill in the blanks in the Escrow Items as provided in the
Subscription Agreement and Article 4.

         7.2      Failure to Collect or Receive Money. Failure of the
Administrative Agent to collect or receive any sums of money to which it might
be entitled to hereunder, or failure to take any action to collect any sums
shall not in anywise prejudice, release or relinquish any of the rights of the
Administrative Agent hereunder.

         7.3      No Duty to Act. Except as provided in Sections 4.2 and 4.3,
the Administrative Agent shall not be under any duty or obligation to take any
action, bring any suit or act in any regard in order to enforce the collection
of any or all of the monies assigned hereunder; and, although it has the right
to do so, failure on the part of the Administrative Agent to do so shall not
relieve, diminish or affect the rights hereunder given or the monies hereby
assigned.

         7.4      Third-Party Beneficiary. The Issuer and each Equity Investor
hereby agree that the Administrative Agent is and shall be a third-party
beneficiary of the Subscription Agreement, and each of them hereby further
agrees and covenants to execute any and all other instruments or documents
necessary to name the Administrative Agent as a third-party beneficiary of the
Subscription Agreement.

<PAGE>   7

                                    SECTION 8
                                  MISCELLANEOUS

         8.1      Agreement Irrevocable. This Agreement may not be revoked by
the Issuer or any Equity Investor and shall continue to be effective with
respect to debt under the Tranche A Term Loans and Tranche B Term Loan arising
or created after any attempted revocation by the Issuer and/or any Equity
Investor. This Agreement shall remain in full force and effect until the
earlier to occur of (a) full and final payment of the Tranche A Term Loans is
made and (b) if Purchase Notices have not been delivered as provided in the
Subscription Agreement, the Expiration Date. 8.2 Issuer's Obligation to Pay.
Anything herein contained shall not in anywise limit or be construed as
limiting the Administrative Agent or the Lenders to collect the Tranche A Term
Loans or any other note, item, sum, or amount secured and to be secured hereby
only out of the revenues, monies, proceeds, benefits, and payments accruing and
to accrue unto the Issuer, under and by virtue of the Subscription Agreement,
but it is expressly understood and provided that all the Indebtedness and
amounts secured and to be secured hereby do, and shall constitute absolute and
unconditional obligations upon the Issuer to pay to the Administrative Agent
and the Lenders.

         8.3      Notices. The Purchase Notices shall be given as provided in
the Subscription Agreement. All notices and other communications provided for
herein (including, without limitation, any modifications of, or waivers or
consents under, this Agreement) shall be given or made by telex, telecopy,
courier or U.S. Mail or in writing and telexed, telecopied, mailed or delivered
to the intended recipient at the "Address for Notices" specified below its name
on the signature pages hereof or in the Loan Documents or, as to any party, at
such other address as shall be designated by such party in a notice to each
other party. Except as otherwise provided in this Agreement, all such
communications shall be deemed to have been duly given when transmitted, if
transmitted before 1:00 p.m. local time on a Business Day (as defined in the
Credit Agreement) (otherwise on the next succeeding Business Day) by telex or
telecopier and evidence or confirmation of receipt is obtained, or personally
delivered or, in the case of a mailed notice, three (3) Business Days after the
date deposited in the mails, postage prepaid, in each case given or addressed
as aforesaid.

         8.4      Amendments, Etc. Any provision of this Agreement or the
Escrow Agreement may be amended, modified or waived with the Issuer's, the
Administrative Agent's and each Equity Investor's prior written consent.

         8.5      Third-Party Beneficiaries. There shall be no third-party
beneficiaries of the Subscription Agreement other than the Administrative Agent
as provided in subsection 7.4 above.

         8.6      Agreements Cumulative. Any and all other instruments executed
or to be executed in connection with or as security for the payment of the
Indebtedness mentioned herein and secured and to be secured hereby, in law or
in equity shall be cumulative one of the other and not exclusive.

<PAGE>   8

         8.7      Governing Law. This Agreement shall be governed by, and
construed in accordance with, the laws of the State of Texas.

         8.8      Counterparts. This Agreement may be executed in any number of
counterparts, all of which taken together shall constitute one and the same
instrument and any of the parties hereto may execute this Agreement by signing
any such counterpart.

         8.9      Section Headings. The words "herein," "hereof," "hereunder"
and other words of similar import when used in this Agreement refer to this
Agreement as a whole, and not to any particular section or subsection. Any
reference herein to a Section or subsection shall be deemed to refer to the
applicable Section or subsection of this Agreement unless otherwise stated
herein. Any reference herein to an annex or exhibit shall be deemed to refer to
the applicable annex or exhibit attached hereto unless otherwise stated herein.
Captions and section headings appearing herein are included solely for
convenience of reference and are not intended to affect the interpretation of
any provision of this Agreement.

         8.10     Successors and Assigns. This Agreement shall be binding upon
and inure to the benefit of the Parties and their respective successors and
permitted assigns.

         8.11     Several Obligations. The respective obligations of the Equity
Investors hereunder are several and not joint. The failure of any Equity
Investor to perform any of its obligations hereunder shall not relieve the
other Equity Investors from any of their respective obligations hereunder.

<PAGE>   9

         IN WITNESS WHEREOF, the Parties have caused this Agreement to be
executed by their duly authorized officers as of the date first above written.

                                       ISSUER:

                                       BARGO ENERGY COMPANY

                                       By:
                                          --------------------------------------
                                       Name:
                                            ------------------------------------
                                       Title:
                                             -----------------------------------

                                       Address for Notices:
                                                           ---------------------

                                                           ---------------------

                                                           ---------------------

                                       ADMINISTRATIVE AGENT:

                                       CHASE BANK OF TEXAS,
                                       NATIONAL ASSOCIATION, as
                                       Administrative Agent

                                       By:
                                          --------------------------------------
                                       Name:
                                            ------------------------------------
                                       Title:
                                             -----------------------------------
                                       Address for Notices:
                                                           ---------------------

                                                           ---------------------

                                                           ---------------------

                                       ENERGY CAPITAL INVESTMENT COMPANY PLC

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

<PAGE>   10

                                       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

                                       EOS PARTNERS, L.P.

                                       By:
                                          --------------------------------------
                                           Brian Young
                                           General Partner

<PAGE>   11

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

                                       By:
                                          --------------------------------------
                                           Brian 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 Young
                                           President

                                       SGC PARTNERS II LLC

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

                                       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

<PAGE>   12

                                       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<PAGE>   1
                                                                    EXHIBIT 10.6

                                ESCROW AGREEMENT

         THIS ESCROW AGREEMENT, dated as of March _____, 2000 ("Escrow
Agreement"), is by and among BARGO ENERGY COMPANY, a Texas corporation
("Issuer"); the persons listed on Exhibit A hereto (each an "Equity Investor"
and collectively the "Equity Investors"); CHASE BANK OF TEXAS, NATIONAL
ASSOCIATION, as administrative agent (in such capacity, the "Administrative
Agent") for each of the lenders (the "Lenders") now or hereafter party to the
hereinafter defined Credit Agreement; and CHASE BANK OF TEXAS, NATIONAL
ASSOCIATION, acting for the benefit of the Issuer, each Equity Investor and the
Administrative Agent (acting in such capacity, the "Escrow Agent").

                                   BACKGROUND

         A. Issuer, Equity Investors and Administrative Agent have entered into
that certain Assignment, Acknowledgment, Agreement and Waiver dated as of March
_____, 2000 (the "Underlying Agreement") whereby, pursuant to the terms thereof,
Issuer, Equity Investors and Administrative Agent agreed to enter into this
Escrow Agreement with the Escrow Agent.

         B. In order to establish the escrow of the Escrow Items (hereinafter
defined) and to effect the provisions of the Underlying Agreement, the parties
hereto have entered into this Escrow Agreement.

                             STATEMENT OF AGREEMENT

         NOW THEREFORE, for good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto, for
themselves, their successors and assigns, hereby agree as follows:

               1. DEFINITIONS. The following terms shall have the following
meanings when used herein:

                  COMMON STOCK means the common stock, $0.01 par value, of the
Issuer.

                  ESCROW ITEMS shall mean the Preferred Stock Certificates, the
Warrants, the Transfer Agent Instructions, the Purchase Notice, and the Purchase
Price deposited with Escrow Agent pursuant to this Escrow Agreement, together
with any interest and other income thereon.

                  PREFERRED STOCK means the Cumulative Redeemable Preferred
Stock, Series C, of the Issuer, $0.01 par value per share.

<PAGE>   2

                  PREFERRED STOCK CERTIFICATES means certificates representing
shares of Preferred Stock one registered in the name of each Equity Investor,
duly executed on behalf of the Issuer, with the number of shares represented by
such certificates left blank.

                  PURCHASE NOTICE means notices executed by the Issuer under the
Subscription Agreement accepting the subscription of the Equity Investors to
purchase shares of Preferred Stock, Common Stock or Warrants to purchase Common
Stock.

                  SUBSCRIPTION AGREEMENT shall mean the Subscription Agreement
dated as of March _____, 2000, between the Issuer and each Equity Investor,
relating to the purchase of shares of Preferred Stock and, at the election of
the Equity Investor, Common Stock or Warrants by such Equity Investor from the
Issuer, and any and all amendments, supplements, modifications, additions,
renewals and/or restatements thereof.

                  SUBSCRIPTION FUNDS shall mean the purchase price of Preferred
Stock and Common Stock or Warrants paid by each Equity Investor pursuant to the
Subscription Agreement.

                  TRANSFER AGENT INSTRUCTIONS means a letter addressed to the
transfer agent for the Common Stock of the Issuer instructing the transfer agent
to issue certificates representing shares of Common Stock to each Equity
Investor pursuant to the Subscription Agreement, and setting forth the number of
shares of Common Stock issued to each Equity Investor.

                  WARRANT AGREEMENT means the warrant agreement to purchase
shares of Common Stock of the Issuer one issued in the name of each Equity
Investor, duly executed on behalf of the Issuer, with the number of shares of
common stock issuable upon exercise of the warrants left blank.

                  WARRANTS means warrants, exercisable for ten years, to
purchase shares of Common Stock of the Issuer for $0.01 per share.

               2. APPOINTMENT OF AND ACCEPTANCE BY ESCROW AGENT. Issuer, each
Equity Investor and Administrative Agent hereby appoint Escrow Agent to serve as
escrow agent hereunder. Escrow Agent hereby accepts such appointment and, upon
deposit of the Escrow Items in accordance with Section 3 below, agrees to hold
and disburse the Escrow Items in accordance with this Escrow Agreement.

               3. DEPOSITS INTO ESCROW OF ESCROW ITEMS.

                  (a)      Issuer has delivered the Preferred Stock
                           Certificates, the Warrant Agreements and the Transfer
                           Agent Instructions to the Escrow Agent to be held on
                           behalf of the Issuer.

                  (b)      Following receipt of the Purchase Notice from the
                           Administrative Agent (in accordance with the
                           Subscription Agreement) and provided (i) the
                           Expiration Date did not occur prior to such delivery
                           and (ii) the conditions

<PAGE>   3

                           precedent to the Equity Investor's obligations set
                           forth in Section 4.5 of the Subscription Notice have
                           been satisfied, each Equity Investor will deposit its
                           Subscription Funds with the Escrow Agent to the
                           following account on or before the Closing Date (as
                           defined in the Subscription Agreement):

                           Chase Bank of Texas, National Association
                           ABA# _________________
                           Account#________________
                           ATTN: ______________________________
                           Re: Bargo Energy Company

               4. DISBURSEMENTS FROM ESCROW. The funds and documents
deposited into Escrow pursuant hereto shall be distributed as follows:

                  (a) Upon receipt, prior to the Expiration Date (as defined in
         the Subscription Agreement), of a certificate executed by an officer of
         the Administrative Agent stating that the Tranche A Equity Subscription
         Date has occurred and that amounts remain outstanding on the Tranche A
         Loan, the Escrow Agent shall deliver the Purchase Notices to the
         Administrative Agent. The Escrow Agent shall send copies of such
         Purchase Notices and the Administrative Agent's certificate delivered
         under this subsection (a) to the Issuer.

                  (b) Upon receipt of Subscription Funds from an Equity Investor
         and a certificate executed by an officer of the Administrative Agent
         which states the number of shares of Preferred Stock and Common Stock
         or Warrants that the Equity Investor has purchased from the Issuer, the
         Escrow Agent shall (i) deliver by wire transfer to the Administrative
         Agent the amount of the Subscription Funds, (ii) complete the Preferred
         Stock Certificate by filling in the number of shares of Preferred Stock
         purchased by the Equity Investor (as indicated in the Administrative
         Agent's certificate) and deliver to such Equity Investor the Preferred
         Stock Certificate, (iii) if the Administrative Agent's certificate
         states that the Equity Investor has purchased Common Stock, complete
         the Transfer Agent Instructions by filling in the number of shares of
         Common Stock purchased (as indicated in such the Administrative Agent's
         certificate) and send to the transfer agent the Transfer Agent
         Instructions instructing the transfer agent to issue certificates to
         the Equity Investor representing shares of Common Stock and (iii) if
         the Administrative Agent's certificate states that the Equity Investor
         has purchased Warrants, complete the Warrant by filling in the number
         of shares of Common Stock subject to the Warrants (as indicated in the
         Administrative Agent's certificate) and send the Warrants to the Equity
         Investor. The Escrow Agent shall send copies of the Preferred Stock
         Certificates, Transfer Agent Instructions or Warrants sent to each
         Equity Investor, as well as a copy of the Administrative Agent's
         certificate delivered under this subsection (b) to the Issuer.

<PAGE>   4

                  (c) Upon receipt of a certificate executed by an officer of
         the Administrative Agent stating that (a) the Tranche A Term Loan has
         been paid in full or (b) the Expiration Date (as defined in the
         Subscription Agreement) has occurred prior to Purchase Notices being
         delivered to the Equity Investors, the Escrow Agent shall deliver all
         Escrowed Items not previously distributed from Escrow to the Issuer.

      5. SUSPENSION OF PERFORMANCE; DISBURSEMENT INTO COURT. If, at any time,
there shall exist any dispute between Issuer, any Equity Investor or the
Administrative Agent with respect to the holding or disposition of any portion
of the Escrow Items or any other obligations of Escrow Agent hereunder, or if at
any time Escrow Agent is unable to determine, to Escrow Agent's sole
satisfaction, the proper disposition of any portion of the Escrow Items or
Escrow Agent's proper actions with respect to its obligations hereunder, or if
the Administrative Agent has not within 30 days of the furnishing by Escrow
Agent of a notice of resignation pursuant to Section 6 hereof, appointed a
successor Escrow Agent to act hereunder, then Escrow Agent may, in its sole
discretion, take either or both of the following actions:

                  a. suspend the performance of any of its obligations
(including without limitation any disbursement obligations) under this Escrow
Agreement until such dispute or uncertainty shall be resolved to the sole
satisfaction of Escrow Agent or until a successor Escrow Agent shall have been
appointed (as the case may be).

                  b. petition (by means of an interpleader action or any other
appropriate method) any court of competent jurisdiction in any venue convenient
to Escrow Agent, for instructions with respect to such dispute or uncertainty,
and to the extent required by law, pay into such court, for holding and
disposition in accordance with the instructions of such court, all Escrow Items
held by it, after deduction and payment to Escrow Agent of all fees and expenses
(including court costs and attorneys' fees) payable to, incurred by, or expected
to be incurred by Escrow Agent in connection with the performance of its duties
and the exercise of its rights hereunder.

         Escrow Agent shall have no liability to Issuer, any Equity Investor,
Administrative Agent or any other person with respect to any such suspension of
performance or disbursement into court, specifically including any liability or
claimed liability that may arise, or be alleged to have arisen, out of or as a
result of any delay in the disbursement of the Escrow Items held by it or any
delay in or with respect to any other action required or requested of Escrow
Agent.

      6. RESIGNATION AND REMOVAL OF ESCROW AGENT. Escrow Agent may resign
from the performance of its duties hereunder at any time by giving ten (10)
days' prior written notice to the Administrative Agent or may be removed, with
or without cause, by Issuer, Equity Investors and Administrative Agent, acting
jointly, at any time by the giving of ten (10) days' prior written notice to
Escrow Agent. Such resignation or removal shall take effect upon the appointment
of a successor Escrow Agent as provided hereinbelow. Upon any such notice of
resignation or removal, the Issuer, Equity Investors and Administrative Agent,
acting jointly, shall appoint a successor Escrow Agent hereunder, which shall be
a commercial bank, trust company or other

<PAGE>   5

financial institution with a combined capital and surplus in excess of
$10,000,000. Upon the acceptance in writing of any appointment as Escrow Agent
hereunder by a successor Escrow Agent, such successor Escrow Agent shall
thereupon succeed to and become vested with all the rights, powers, privileges
and duties of the retiring Escrow Agent, and the retiring Escrow Agent shall be
discharged from its duties and obligations under this Escrow Agreement, but
shall not be discharged from any liability for actions taken as Escrow Agent
hereunder prior to such succession. After any retiring Escrow Agent's
resignation or removal, the provisions of this Escrow Agreement shall inure to
its benefit as to any actions taken or omitted to be taken by it while it was
Escrow Agent under this Escrow Agreement. The retiring Escrow Agent shall
transmit all records pertaining to the Escrow Items and shall deliver all Escrow
Items held by it to the successor Escrow Agent, after making copies of such
records as the retiring Escrow Agent deems advisable and after deduction and
payment to the retiring Escrow Agent of all fees and expenses (including court
costs and attorneys' fees) payable to, incurred by, or expected to be incurred
by the retiring Escrow Agent in connection with the performance of its duties
and the exercise of its rights hereunder.

               7. LIABILITY OF ESCROW AGENT.

                  a. Escrow Agent shall have no liability or obligation with
respect to the Escrow Items except for Escrow Agent's willful misconduct or
gross negligence. Escrow Agent's sole responsibility shall be for the
safekeeping, and disbursement of the Escrow Items in accordance with the terms
of this Escrow Agreement. Escrow Agent shall have no implied duties or
obligations and shall not be charged with knowledge or notice of any fact or
circumstance not specifically set forth herein. Escrow Agent may rely upon any
instrument, not only as to its due execution, validity and effectiveness, but
also as to the truth and accuracy of any information contained therein, which
Escrow Agent shall in good faith believe to be genuine, to have been signed or
presented by the person or parties purporting to sign the same and to conform to
the provisions of this Escrow Agreement. In no event shall Escrow Agent be
liable for incidental, indirect, special, consequential or punitive damages.
Escrow Agent shall not be obligated to take any legal action or commence any
proceeding in connection with the Escrow Items, any account in which Escrow
Items are deposited, this Escrow Agreement or the Underlying Agreement, or to
appear in, prosecute or defend any such legal action or proceeding. Escrow Agent
may consult legal counsel selected by it in the event of any dispute or question
as to the construction of any of the provisions hereof or of any other agreement
or of its duties hereunder, or relating to any dispute involving any party
hereto, and shall incur no liability and shall be fully indemnified from any
liability whatsoever in acting in accordance with the opinion or instruction of
such counsel. Issuer and Equity Investors, jointly and severally, shall promptly
pay, upon demand, the reasonable fees and expenses of any such counsel.

         b. The Escrow Agent is authorized, in its sole discretion, to comply
with orders issued or process entered by any court with respect to the Escrow
Items, without determination by the Escrow Agent of such court's jurisdiction in
the matter. If any portion of the Escrow Items is at any time attached,
garnished or levied upon under any court order, or in case the payment,
assignment, transfer, conveyance or delivery of any such property shall be
stayed or

<PAGE>   6

enjoined by any court order, or in case any order, judgment or decree shall be
made or entered by any court affecting such property or any part thereof, then
and in any such event, the Escrow Agent is authorized, in its sole discretion,
to rely upon and comply with any such order, writ, judgment or decree which it
is advised by legal counsel selected by it is binding upon it without the need
for appeal or other action; and if the Escrow Agent complies with any such
order, writ, judgment or decree, it shall not be liable to any of the parties
hereto or to any other person or entity by reason of such compliance even though
such order, writ, judgment or decree may be subsequently reversed, modified,
annulled, set aside or vacated.

               8. INDEMNIFICATION OF ESCROW AGENT. From and at all times
after the date of this Escrow Agreement, Issuer and Equity Investors, jointly
and severally, shall, to the fullest extent permitted by law and to the extent
provided herein, indemnify and hold harmless Escrow Agent and each director (in
his or her capacity as a director of Escrow Agent), officer, employee, attorney,
agent and affiliate of Escrow Agent (collectively, the "Indemnified Parties")
against any and all actions, claims (whether or not valid), losses, damages,
liabilities, costs and expenses of any kind or nature whatsoever (including
without limitation reasonable attorneys' fees, costs and expenses) incurred by
or asserted against any of the Indemnified Parties from and after the date
hereof, whether direct, indirect or consequential, as a result of or arising
from or in any way relating to any claim, demand, suit, action or proceeding
(including any inquiry or investigation) by any person, including without
limitation Issuer or any Equity Investor, whether threatened or initiated,
asserting a claim for any legal or equitable remedy against any person under any
statute or regulation, including, but not limited to, any federal or state
securities laws, or under any common law or equitable cause or otherwise,
arising from or in connection with the negotiation, preparation, execution,
performance or failure of performance of this Escrow Agreement or any
transactions contemplated herein, whether or not any such Indemnified Party is a
party to any such action, proceeding, suit or the target of any such inquiry or
investigation; provided, however, that no Indemnified Party shall have the right
to be indemnified hereunder for any liability finally determined by a court of
competent jurisdiction, subject to no further appeal, to have resulted solely
from the gross negligence or willful misconduct of such Indemnified Party. If
any such action or claim shall be brought or asserted against any Indemnified
Party, such Indemnified Party shall promptly notify Issuer and Equity Investors
in writing, and Issuer and Equity Investors shall assume the defense thereof,
including the employment of counsel and the payment of all expenses. Such
Indemnified Party shall, in its sole discretion, have the right to employ
separate counsel (who may be selected by such Indemnified Party in its sole
discretion) in any such action and to participate in the defense thereof, and
the fees and expenses of such counsel shall be paid by such Indemnified Party,
except that Issuer and Equity Investors shall be required to pay such fees and
expenses if (a) Issuer and/or Equity Investors agree to pay such fees and
expenses, or (b) Issuer and/or Equity Investors shall fail to assume the defense
of such action or proceeding or shall fail, in the sole discretion of such
Indemnified Party, to employ counsel satisfactory to the Indemnified Party in
any such action or proceeding, (c) Issuer and/or Equity Investors is the
plaintiff in any such action or proceeding or (d) the named or potential parties
to any such action or proceeding (including any potentially impleaded parties)
include both Indemnified Party and Issuer and/or Equity Investors, and
Indemnified Party shall have been advised by counsel that there may be one or
more legal defenses available to it which are

<PAGE>   7

different from or additional to those available to Issuer and/or Equity
Investors. Issuer and/or Equity Investors shall be jointly and severally liable
to pay fees and expenses of counsel pursuant to the preceding sentence, except
that any obligation to pay under clause (a) shall apply only to the party so
agreeing. All such fees and expenses payable by Issuer and/or Equity Investors
pursuant to the foregoing sentence shall be paid from time to time as incurred,
both in advance of and after the final disposition of such action or claim. All
of the foregoing losses, damages, costs and expenses of the Indemnified Parties
shall be payable by Issuer and/or Equity Investors, jointly and severally, to
the extent of the Escrow Items upon demand by such Indemnified Party. Upon
exhaustion of the Escrow Items, the indemnification obligations of Issuer and
Equity Investors hereunder shall be borne by Issuer and Equity Investors,
jointly and severally. The obligations of Issuer and Equity Investors under this
Section 8 shall survive any termination of this Escrow Agreement, and the
resignation or removal of Escrow Agent shall be independent of any obligation of
the Escrow Agent.

         The parties agree that neither the payment by Issuer or Equity
Investors of any claim by Escrow Agent for indemnification hereunder nor the
disbursement of any amounts to Escrow Agent from the Escrow Items in respect of
a claim by Escrow Agent for indemnification shall impair, limit, modify or
affect, as between Issuer and Equity Investors, the respective rights and
obligations of Issuer, on the one hand, and Equity Investors, on the other hand,
under the Underlying Agreement.

         9. FEES AND EXPENSES OF ESCROW AGENT. None.

         10. NOTICE. All notices required to be given hereunder shall be in
writing, shall be given by telecopier, with original to follow, and shall be
deemed given when received by telecopier at the address for notices specified
under the parties signatures on the signature pages hereof until such time as
the parties hereto designate a different or additional address or addresses.

         11. AMENDMENT OR WAIVER. This Escrow Agreement may be changed, waived,
discharged or terminated only by a writing signed by the Issuer, Equity
Investors, Administrative Agent and Escrow Agent. No delay or omission by any
party in exercising any right with respect hereto shall operate as a waiver. A
waiver on any one occasion shall not be construed as a bar to, or waiver of, any
right or remedy on any future occasion.

         12. SEVERABILITY. To the extent any provision of this Escrow Agreement
is prohibited by or invalid under applicable law, such provision shall be
ineffective to the extent of such prohibition or invalidity, without
invalidating the remainder of such provision or the remaining provisions of this
Escrow Agreement.

         13. GOVERNING LAW. This Escrow Agreement shall be construed and
interpreted in accordance with the internal laws of the State of Texas.

         14. ENTIRE AGREEMENT. This Escrow Agreement [and the Underlying
Agreement] constitute(s) the entire agreement between the parties relating to
the holding and disbursement of

<PAGE>   8

the Escrow Items and sets forth in their entirety the obligations and duties of
Escrow Agent with respect to the Escrow Items.

         15. BINDING EFFECT. All of the terms of this Escrow Agreement, as
amended from time to time, shall be binding upon, inure to the benefit of and be
enforceable by the respective heirs, successors and assigns of Issuer, Equity
Investors, Administrative Agent and Escrow Agent.

         16. EXECUTION IN COUNTERPARTS. This Escrow Agreement may be executed in
two or more counterparts, which when so executed shall constitute one and the
same agreement or direction. This Escrow Agreement and any document in
connection herewith may be sent by facsimile transmission, which when so sent
shall be deemed an original executed document delivered for all purposes hereof.

         17. TERMINATION. Upon the first to occur of the disbursement of all
Escrow Items or the disbursement of all Escrow Items into court pursuant to
Section 5 hereof, this Escrow Agreement shall terminate and Escrow Agent shall
have no further obligation or liability whatsoever with respect to this Escrow
Agreement or the Escrow Items.

<PAGE>   9

         IN WITNESS WHEREOF, the parties hereto have caused this Escrow
Agreement to be executed under seal as of the date first above written.

                    ISSUER:

                    BARGO ENERGY COMPANY

                    By:
                       ---------------------------------
                    Name:
                         -------------------------------
                    Title:
                          ------------------------------

                    Address for Notices:

                    ------------------------------------

                    ------------------------------------

                    ------------------------------------

                    ENERGY CAPITAL INVESTMENT CO., 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

<PAGE>   10

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

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

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

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

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

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

<PAGE>   11

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

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 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

<PAGE>   12

ADMINISTRATIVE AGENT:

CHASE BANK OF TEXAS, NATIONAL ASSOCIATION,
as Administrative Agent

By:
   ---------------------------------
Name:
     -------------------------------
Title:
      ------------------------------

Address for Notices:

------------------------------------

------------------------------------

------------------------------------

ESCROW AGENT:

CHASE BANK OF TEXAS, NATIONAL ASSOCIATION,
as Escrow Agent

By:
   ---------------------------------
Name:
     -------------------------------
Title:
      ------------------------------

Address for Notices:

------------------------------------

------------------------------------

------------------------------------

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