Document:

<PAGE>   1
                                                                    EXHIBIT 10.2

                         Effective as of August 24, 2000

Encore Operating, L.P.
c/o Encore Acquisition Partners, Inc.
777 Main Street, Suite 1400
Fort Worth, Texas 76102
Attn:    Sam Smith

     Re:  Credit Agreement dated as of May 7, 1999, by and among Encore
          Operating, L.P. ("Borrower"), Encore Acquisition Partners, Inc., as
          Parent Guarantor, NationsBank, N.A. (predecessor by merger to Bank of
          America, N.A.), as Administrative Agent, First Union National Bank, as
          Syndication Agent, BankBoston, N.A. (predecessor in interest to Fleet
          National Bank), as Documentary Agent and the financial institutions
          listed on Schedule 1 thereto, as Banks ("Banks") (as amended, the
          "Credit Agreement"); unless otherwise defined herein, all terms used
          herein with their initial letter capitalized shall have the meaning
          set forth in the Credit Agreement.

Gentlemen:

         Pursuant to Section 5.2 of the Credit Agreement, and subject to the
terms and conditions set forth below, the Borrowing Base shall be $180,000,000
effective August 24, 2000 and continuing until the next Redetermination of the
Borrowing Base thereafter (the "Pioneer Borrowing Base Increase"). Banks further
agree that the Borrowing Base will be increased to $200,000,000 simultaneously
with the payment in full of the Burlington Note (as herein defined) and subject
to the other terms and conditions set forth herein (the "Burlington Borrowing
Base Increase"). Borrower and Banks agree that neither Redetermination provided
for herein shall be construed or deemed to be a Special Redetermination for
purposes of Section 5.3 of the Credit Agreement.

         The Pioneer Borrowing Base Increase provided for herein is based on,
and subject to, the satisfaction of the following conditions:

         (A)      Borrower shall have completed the purchase (the "Subject
                  Acquisition") of the properties and interests (collectively,
                  the "Subject Properties") described in that certain Purchase
                  and Sale Agreement (as amended, the "Pioneer PSA") dated as of
                  June 9, 2000, by and between Pioneer Natural Resources USA,
                  Inc., a Delaware corporation, as seller, and Borrower, as
                  purchaser (the Subject Properties to be purchased by Borrower
                  pursuant to such Pioneer PSA to include, without limitation,
                  the Assets under and as defined in such Pioneer PSA), all in
                  accordance with the terms of the Pioneer PSA, and as a result

<PAGE>   2

Encore Operating, L.P.
As of August 24, 2000
Page 2

                  thereof, Borrower shall have acquired good and defensible
                  title to all such Subject Properties, free and clear of all
                  Liens except Permitted Encumbrances.

         (B)      Administrative Agent and its counsel shall have completed a
                  review of title to that portion of the Subject Properties that
                  results in Administrative Agent and its counsel having
                  completed a review of not less than seventy percent (70%) of
                  the Recognized Value of all Proved Mineral Interests owned by
                  Borrower after giving effect to the Subject Acquisition, and
                  such review shall not have revealed any condition or
                  circumstance which would reflect that, upon completion of the
                  Subject Acquisition, the representations and warranties
                  contained in Section 8.9 of the Credit Agreement are
                  inaccurate in any respect.

         (C)      Administrative Agent and it counsel shall have been provided
                  with, and shall have completed a review of, the environmental
                  reports required by Section 9.13 of the Credit Agreement with
                  respect to the Subject Properties and such review shall not
                  have revealed any condition or circumstance which would
                  reflect that, upon completion of the Subject Acquisition, the
                  representations and warranties contained in Section 8.14 of
                  the Credit Agreement are inaccurate in any respect.

         (D)      Administrative Agent shall have been provided with a copy of
                  the Pioneer PSA and all other material documents, instruments
                  and agreements executed and/or delivered by any Credit Party
                  in connection with the Subject Acquisition, together with a
                  certificate from an Authorized Officer of Borrower (or the
                  general partner of Borrower) certifying that such copies are
                  accurate and complete and represent the complete understanding
                  and agreement of the parties with respect to the subject
                  matter thereof.

         (E)      All fees and expenses of Administrative Agent and its
                  Affiliates in connection with the Pioneer Borrowing Base
                  Increase shall have been paid, including, without limitation,
                  the payment to Administrative Agent of a fee in the amount of
                  $37,500 for the ratable benefit of the Banks.

         (F)      The representations and warranties of each Credit Party
                  contained in the Credit Agreement and the other Loan Papers
                  shall be true and correct in all material respects prior to,
                  and upon completion of, the Subject Acquisition, with the same
                  effect as though such representations and warranties had been
                  made immediately prior to, and immediately upon completion of,
                  the Subject Acquisition or, if such representations and
                  warranties are expressly limited to particular dates, as of
                  such particular dates.

<PAGE>   3

Encore Operating, L.P.
As of August 24, 2000
Page 3

         (G)      Immediately prior to, and immediately upon completion of, the
                  Subject Acquisition, no Default or Event of Default shall have
                  occurred and be continuing.

         The Burlington Borrowing Base Increase provided for herein is based on,
and subject to, the satisfaction of the conditions set forth in that certain
letter agreement dated effective as of June 1, 2000 by and among Borrower and
Banks, and, without limiting the foregoing, the satisfaction of the following
conditions:

         (A)      Borrower shall have paid in full that certain Purchase Money
                  Note (the "Burlington Note") dated March 1, 2000, payable by
                  Borrower to Burlington Resources Oil & Gas Company
                  ("Burlington") in the original principal amount of US
                  $35,200,000, and such payment in full shall have been made on
                  or before the next Redetermination hereafter.

         (B)      Borrower shall have obtained a full and complete release of
                  (i) that certain Mortgage, Assignment, Security Agreement and
                  Financing Statement dated as of March 1, 2000 executed by
                  Borrower for the benefit of Burlington, and (ii) all Liens
                  encumbering the Mineral Interests described therein.

         (C)      All fees and expenses of Administrative Agent and its
                  Affiliates in connection with the Burlington Borrowing Base
                  Increase shall have been paid, including, without limitation,
                  the payment to Administrative Agent of a fee in the amount of
                  $50,000 for the ratable benefit of the Banks.

         (D)      No Default or Event of Default shall have occurred which is
                  continuing.

         (E)      The representations and warranties of each Credit Party
                  contained in the Credit Agreement and the other Loan Papers
                  shall be true and correct in all material respects prior to,
                  and immediately upon giving effect to, the Burlington
                  Borrowing Base Increase, with the same effect as though said
                  representations and warranties had been made immediately prior
                  to, and immediately after giving effect to, the Burlington
                  Borrowing Base Increase or, if such representations and
                  warranties are expressly limited to particular dates, as of
                  such particular dates.

                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]

<PAGE>   4

Encore Operating, L.P.
As of August 24, 2000
Page 4

         Please evidence your acknowledgment of, and agreement to, the foregoing
by executing this letter in the space provided below. This letter may be
executed in counterparts, and all parties need not execute the same counterpart.
Facsimiles will be effective as originals.

                                       Very truly yours,

                                       BANK OF AMERICA, N.A.,
                                       successor by merger to NationsBank, N.A.

                                       By: /s/ J. SCOTT FOWLER
                                           -------------------------------------
                                           J. Scott Fowler,
                                           Managing Director

                                       FIRST UNION NATIONAL BANK

                                       By: /s/
                                           -------------------------------------
                                       Name:
                                            ------------------------------------
                                       Title:
                                             -----------------------------------

                                       FLEET NATIONAL BANK,
                                       formerly BankBoston, N.A.

                                       By: /s/
                                           -------------------------------------
                                       Name:
                                            ------------------------------------
                                       Title:
                                             -----------------------------------

                                       THE FROST NATIONAL BANK

                                       By: /s/
                                           -------------------------------------
                                       Name:
                                            ------------------------------------
                                       Title:
                                             -----------------------------------

<PAGE>   5

Encore Operating, L.P.
As of August 24, 2000
Page 4

                                       COMERICA BANK-TEXAS

                                       By: /s/
                                           -------------------------------------
                                       Name:
                                            ------------------------------------
                                       Title:
                                             -----------------------------------

                                       CIBC INC.

                                       By: /s/
                                           -------------------------------------
                                       Name:
                                            ------------------------------------
                                       Title:
                                             -----------------------------------

                                       Acknowledged and agreed effective as of
                                       the 24th day of August, 2000

                                       ENCORE OPERATING, L.P.,
                                       a Texas limited partnership

                                       By: EAP Operating, Inc.,
                                       a Delaware corporation,
                                       its sole general partner

                                       By: /s/
                                           -------------------------------------
                                       Name:
                                            ------------------------------------
                                       Title:
                                             -----------------------------------<PAGE>   1

                                                                    EXHIBIT 10.3

                                PLEDGE AGREEMENT

         THIS PLEDGE AGREEMENT (this "Agreement") is made as of May 7, 1999 by
Encore Acquisition Partners, Inc., a Delaware corporation (herein called
"Pledgor"), in favor of NationsBank, N.A., as Administrative Agent for the
ratable benefit of Banks (as defined below) (herein called "Pledgee").

                                   WITNESSETH:

         WHEREAS, Pledgor, Encore Operating, L.P., a Texas limited partnership
("Borrower"), Pledgee, First Union National Bank, as Syndication Agent,
BankBoston, N.A., as Documentary Agent, and Banks are parties to a Credit
Agreement dated as of May 7, 1999, pursuant to which Banks have made a revolving
credit loan to Borrower and agreed to issue and participate in letters of credit
issued on behalf of Borrower (herein called the "Credit Agreement"); and

         WHEREAS, it is a condition to the agreement of Banks to extend (and/or
to continue to extend) credit under the Credit Agreement that Pledgor execute
and deliver this Agreement in favor of Pledgee for the benefit of Banks.

         NOW, THEREFORE, in consideration of the premises and in order to induce
Banks to extend (and/or to continue to extend) credit under the Credit
Agreement, Pledgor hereby agrees with Pledgee as follows:

                                    ARTICLE I

                           Definitions and References

         Section 1.1. General Definitions. As used herein, the terms
"Agreement," "Credit Agreement," "Borrower," "Pledgee," and "Pledgor," shall
have the meanings indicated above, and the following terms shall have the
following meanings:

         "Bank" means any financial institution reflected on Schedule 1 to the
Credit Agreement and its successors and assigns, and "Banks" shall mean all
Banks.

         "Code "means the Uniform Commercial Code in effect in the State of
Texas on the date hereof.

         "Collateral" means all property of whatever type, in which Pledgee at
any time has a security interest pursuant to Section 2.1.

         "Commitment" means the agreement or commitment by Banks to make loans
or otherwise extend credit to Borrower under the Credit Agreement, and any other
agreement, commitment, statement of terms or other document contemplating the
making of loans or advances or other extension of credit by Banks to or for the
account of Borrower which is now or at any time hereafter intended to be secured
by the Collateral under this Agreement.

         "Obligation Documents" means the Credit Agreement, the Note, the other
Loan Papers, and all other documents and instruments under, by reason of which,
or pursuant to which, any or

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all of the Obligations are evidenced, governed, secured, or otherwise dealt
with, and all other agreements, certificates, and other documents, instruments
and writings heretofore or hereafter delivered in connection herewith or
therewith.

         "Obligations" means all present and future indebtedness, obligations
and liabilities of whatever type which are or shall be secured pursuant to
Section 2.2.

         "Other Liable Party" means any Person, other than Borrower, who may now
or may at any time hereafter be primarily or secondarily liable for any of the
Obligations or who may now or may at any time hereafter have granted to Pledgee
or Banks a Lien upon any property as security for the Obligations.

         "Pledged Equity" the meaning given it in Section 2.1.

         Section 1.2. Other Definitions. Reference is hereby made to the Credit
Agreement for a statement of the terms thereof. All capitalized terms used in
this Agreement which are defined in the Credit Agreement and not otherwise
defined herein shall have the same meanings herein as set forth therein. All
terms used in this Agreement which are defined in the Code and not otherwise
defined herein or in the Credit Agreement shall have the same meanings herein as
set forth therein, except where the context otherwise requires.

         Section 1.3. Exhibits. All exhibits attached to this Agreement are a
part hereof for all purposes.

         Section 1.4. Amendment of Defined Instruments. Unless the context
otherwise requires or unless otherwise provided herein, references in this
Agreement to a particular agreement, instrument or document also refer to and
include all renewals, extensions, amendments, modifications, supplements or
restatements of any such agreement, instrument or document, provided that
nothing contained in this Section 1.4 shall be construed to authorize any Person
to execute or enter into any such renewal, extension, amendment, modification,
supplement or restatement.

         Section 1.5. References and Titles. All references in this Agreement to
Exhibits, Articles, Sections, subsections, and other subdivisions refer to the
Exhibits, Articles, Sections, subsections and other subdivisions of this
Agreement unless expressly provided otherwise. Titles appearing at the beginning
of any subdivision are for convenience only and do not constitute any part of
any such subdivision and shall be disregarded in construing the language
contained in this Agreement. The words "this Agreement," "herein," "hereof,"
"hereby," "hereunder" and words of similar import refer to this Agreement as a
whole and not to any particular subdivision unless expressly so limited. The
phrases "this Section" and "this subsection" and similar phrases refer only to
the Sections or subsections hereof in which the phrase occurs. The word "or" is
not exclusive, and the word "including" (in all of its forms) means "including
without limitation". Pronouns in masculine, feminine and neuter gender shall be
construed to include any other gender, and words in the singular form shall be
construed to include the plural and vice versa unless the context otherwise
requires.

                                       2
<PAGE>   3

                                   ARTICLE II

                                Security Interest

         Section 2.1. Grant of Security Interest. As collateral security for all
of the Obligations, Pledgor hereby pledges and assigns to Pledgee and grants to
Pledgee a continuing first priority security interest for the benefit of Banks
in and to all of the following rights, interests and property:

         (a) all of the issued and outstanding shares of capital stock,
membership interests or partnership interests of each Subsidiary of Pledgor now
owned or hereafter acquired by Pledgor including, without limitation, the
shares, membership interests or partnership interests of each Subsidiary of
Pledgor owned by Pledgor on the date hereof (all of the foregoing being herein
sometimes called the "Pledged Equity");

         (b) any and all proceeds or other sums arising from or by virtue of,
and all dividends and distributions (cash or otherwise) payable and/or
distributable with respect to, all or any of the Pledged Equity described in
clause (a) preceding; and

         (c) all cash, securities, dividends and other property at any time and
from time to time receivable or otherwise distributed in respect of or in
exchange for any or all of the Pledged Equity described in clause (a) hereof and
any other property substituted or exchanged therefor.

         Section 2.2. Obligations Secured. The security interest created hereby
in the Collateral constitutes continuing collateral security for all of the
following obligations, indebtedness and liabilities, whether now existing or
hereafter incurred:

         (a) Credit Agreement Indebtedness. The payment by Borrower, as and when
due and payable, of all amounts from time to time owing by Borrower under or in
respect of the Credit Agreement, the Notes or any of the other Obligation
Documents.

         (b) Renewals. All renewals, extensions, amendments, modifications,
supplements, or restatements of, or substitutions for, any of the foregoing.

         (c) Performance. The due performance and observance by Borrower of all
of its other obligations from time to time existing under or in respect of any
of the Obligation Documents.

         (d) Hedge Transactions. The payment and performance of any and all
present or future obligations of Borrower according to the terms of any present
or future Hedge Transaction, including, without limitation, any present or
future swap agreements, cap, floor, collar, exchange, transaction, forward
agreement or other exchange or protection agreements relating to crude oil,
natural gas or other Hydrocarbons, or any option with respect to any such
transaction now existing or hereafter entered into between and/or among Pledgor,
Borrower, Pledgee, any Bank or any affiliate of any of the foregoing.

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<PAGE>   4

                                   ARTICLE III

                    Representations Warranties and Covenants

         Section 3.1. Representations and Warranties. Pledgor represents and
warrants as follows:

         (a) Ownership and Liens. Pledgor has good and marketable title to the
Collateral free and clear of all Liens, encumbrances or adverse claims, except
for the security interest created by this Agreement. No effective financing
statement or other instrument similar in effect covering all or any part of the
Collateral is on file in any recording office except such as have been filed in
favor of Pledgee relating to this Agreement.

         (b) No Conflicts or Consents. Neither the ownership or the intended use
of the Collateral by Pledgor, nor the grant of the security interest by Pledgor
to Pledgee herein, nor the exercise by Pledgee of its rights or remedies
hereunder, will (i) conflict with any provision of (a) any domestic or foreign
law, statute, rule or regulation, (b) the articles of incorporation, certificate
of limited partnership, partnership agreement, regulations, charter or bylaws of
Pledgor, or (c) any agreement, judgment, license, order or permit applicable to
or binding upon Pledgor, or (ii) result in or require the creation of any Lien,
charge or encumbrance upon any assets or properties of Pledgor except as
expressly contemplated in the Obligation Documents. Except as expressly
contemplated in the Obligation Documents, no consent, approval, authorization or
order of, and no notice to or filing with, any court, Governmental Authority or
third party is required in connection with the grant by Pledgor of the security
interest herein, or the exercise by Pledgee of its rights and remedies
hereunder.

         (c) Security Interest. Pledgor has and will have at all times full
right, power and authority to grant a security interest in the Collateral to
Pledgee in the manner provided herein, free and clear of any Lien, adverse
claim, or encumbrance. This Agreement creates a valid and binding security
interest in favor of Pledgee in the Collateral securing the Obligations. The
taking possession by Pledgee (for the ratable benefit of Banks) of all
certificates, instruments and cash constituting Collateral from time to time and
the filing of the financing statements delivered concurrently herewith by
Pledgor to Pledgee will perfect, and establish the first priority of, Pledgee's
security interest hereunder in the Collateral securing the Obligations. No
further or subsequent filing, recording, registration, other public notice or
other action is necessary or desirable to perfect or otherwise continue,
preserve or protect such security interest except for continuation statements or
filings as contemplated in Section 3.3(b).

         (d) Pledged Equity. (i) Pledgor is the legal and beneficial owner of
the Pledged Equity issued by each Subsidiary of Pledgor, (ii) the Pledged Equity
is duly authorized and issued, fully paid and non-assessable, and all
documentary, stamp or other Taxes or fees owing in connection with the issuance,
transfer and/or pledge thereof hereunder have been paid, (iii) no dispute, right
of setoff, counterclaim or defense exists with respect to all or any part of the
Pledged Equity, (iv) the Pledged Equity is free and clear of all Liens, options,
warrants, puts, calls or other rights of third Persons, and restrictions, other
than (a) those Liens arising under this Agreement or any other of the Loan
Papers and Liens for Taxes not yet due and payable, and (b) restrictions on
transferability imposed by applicable state and federal securities Laws, (v)
Pledgor has full right and authority to pledge the Pledged Equity for the
purposes and upon the terms set out herein, (vi) certificates (or other evidence
acceptable to Pledgee) representing the

                                       4
<PAGE>   5

Pledged Equity have been delivered to Pledgee, together with a duly executed
blank stock power (as applicable) with signatures guaranteed, for each
certificate, (vii) the Pledged Equity constitutes all of the issued and
outstanding capital stock, membership interests or partnership interests of each
Subsidiary of Pledgor of every class, and (viii) no Subsidiary of Pledgor has
issued, and there are not outstanding, any options, warrants or other rights to
acquire capital stock, membership interests, or partnership interests of any
Subsidiary of Pledgor.

         Section 3.2. Affirmative Covenants. Unless Pledgee shall otherwise
consent in writing, Pledgor will at all times comply with the covenants
contained in this Section 3.2 from the date hereof and so long as any part of
the Obligations or Commitments is outstanding.

         (a) Ownership and Liens. Pledgor will maintain good and marketable
title to all Collateral free and clear of all Liens encumbrances or adverse
claims, except for the security interest created by this Agreement and the
security interests and other encumbrances expressly permitted by the Credit
Agreement. Pledgor will cause to be terminated any financing statement or other
registration with respect to the Collateral, except such as may exist or as may
have been filed in favor of Pledgee. Pledgor will defend Pledgee's right, title
and special property and security interest in and to the Collateral against the
claims of any Person.

         (b) Further Assurances. Pledgor will, at its expense and at any time
and from time to time, promptly execute and deliver all further instruments and
documents and take all further action that may be necessary or desirable or that
Pledgee may request in order (i) to perfect and protect the security interest
created or purported to be created hereby and the first priority of such
security interest; (ii) to enable Pledgee to exercise and enforce its rights and
remedies hereunder in respect of the Collateral; or (iii) to otherwise effect
the purposes of this Agreement, including, without limitation: (A) executing and
filing such financing or continuation statements, or amendments thereto, as may
be necessary or desirable or that Pledgee may request in order to perfect and
preserve the security interest created or purported to be created hereby; and
(B) furnishing to Pledgee from time to time statements and schedules further
identifying and describing the Collateral and such other reports in connection
with the Collateral as Pledgee may reasonably request, all in reasonable detail.

         (c) Delivery of Pledged Equity. All certificates, instruments and
writings evidencing the Pledged Equity shall be delivered to Pledgee on or prior
to the execution and delivery of this Agreement. All other certificates,
instruments and writings hereafter evidencing or constituting Pledged Equity
shall be delivered to Pledgee promptly upon the receipt thereof by or on behalf
of Pledgor. All such Pledged Equity shall be held by or on behalf of Pledgee
pursuant hereto and shall be delivered in the same manner and with the same
effect as described in Section 2.1 and Section 3.1 hereof. Upon delivery, such
equity interests shall thereupon constitute "Pledged Equity" and shall be
subject to the Liens herein created, for the purposes and upon the terms and
conditions set forth in this Agreement and the other Loan Papers.

         (d) Proceeds of Pledged Equity. If Pledgor shall receive, by virtue of
its being or having been an owner of any Pledged Equity, any (i) shares of
capital stock, membership interests and/or partnership interests (including any
certificate representing any shares of capital stock, membership interests
and/or partnership interests or distribution in connection with any increase or
reduction of capital, reorganization, reclassification, merger, consolidation,
sale of assets, or spinoff or split-off), promissory note or other instrument or
writing; (ii) option or right,

                                       5
<PAGE>   6

whether as an addition to, substitution for, or in exchange for, any Pledged
Equity or otherwise; (iii) dividends payable in cash (except such dividends
permitted to be retained by Pledgor pursuant to Section 4.7 hereof) or in
securities or other property; or (iv) dividends or other distributions in
connection with a partial or total liquidation or dissolution or in connection
with a reduction of capital, capital surplus or paid-in surplus, Pledgor shall
receive the same in trust for the benefit of Pledgee, shall segregate it from
Pledgor's other property, and shall promptly deliver it to Pledgee in the exact
form received, with any necessary endorsement or appropriate stock powers duly
executed in blank, to be held by Pledgee as Collateral.

         (e) Status of Pledged Equity. The certificates (or other instruments
and writings) evidencing the Pledged Equity shall at all times be valid and
genuine and shall not be altered. The Pledged Equity at all times shall be duly
authorized, validly issued, fully paid, and non-assessable, shall not be issued
in violation of the pre-emptive rights of any Person or of any agreement by
which Pledgor or any of its Subsidiaries is bound, and, except for the
partnership agreement, regulations or bylaws of Pledgor, shall not be subject to
any restrictions or conditions with respect to the transfer, voting or capital
of any Pledged Equity.

         Section 3.3. Negative Covenants. Unless Pledgee shall otherwise consent
in writing, Pledgor will at all times comply with the covenants contained in
this Section 3.3 from the date hereof and so long as any part of the Obligations
or the Commitments is outstanding.

         (a) Transfer or Encumbrance. Pledgor will not sell, assign (by
operation of law or otherwise), transfer, exchange, lease or otherwise dispose
of any of the Collateral, nor will Pledgor grant a Lien upon or execute, file or
record any financing statement or other registration with respect to the
Collateral, nor will Pledgor allow any such Lien, financing statement, or other
registration to exist or deliver actual or constructive possession of the
Collateral to any other Person other than Liens in favor of Pledgee.

         (b) Financing Statement Filings. Pledgor recognizes that financing
statements pertaining to the Collateral have been or may be filed where Pledgor
maintains any Collateral, has its records concerning any Collateral or has its
chief executive office or chief place of business. Without limitation of any
other covenant herein, Pledgor will not cause or permit any change to be made in
its name, identity or corporate, partnership or limited liability company
structure, or any change to be made to a jurisdiction other than as represented
in Section 3.1 hereof in (i) the location of any records concerning any
Collateral, or (ii) in the location of its chief executive office or chief place
of business, unless Pledgor shall have notified Pledgee of such change at least
thirty (30) days prior to the effective date of such change, and shall have
first taken all action required by Pledgee for the purpose of further perfecting
or protecting the security interest in favor of Pledgee in the Collateral. In
any notice furnished pursuant to this subsection, Pledgor will expressly state
that the notice is required by this Agreement and contains facts that may
require additional filings of financing statements or other notices for the
purposes of continuing perfection of Pledgee's security interest in the
Collateral.

         (c) Impairment of Security Interest. Pledgor will not take or fail to
take any action which would in any manner impair the enforceability of Pledgee's
security interest in any Collateral.

                                       6
<PAGE>   7

         (d) Dilution of Pledged Equity. Pledgor will not permit the issuance of
(i) any additional shares of capital stock, membership interests or partnership
interests of any class of any of its Subsidiaries (unless immediately upon
issuance the same are pledged and delivered to Pledgee pursuant to the terms
hereof), (ii) any securities convertible voluntarily by the holder thereof or
automatically upon the occurrence or non-occurrence of any event or condition
into, or exchangeable for, any such capital stock, membership interests or
partnership interests, or (iii) any warrants, options, contracts or other
commitments entitling any Person to purchase or otherwise acquire any such
capital stock; membership interests or partnership interests of any Subsidiary
of Pledgor.

         (e) Restrictions on Pledged Equity. Except for the partnership
agreement, regulations or bylaws of each Subsidiary of Pledgor, Pledgor will not
enter into any agreement creating, or otherwise permit to exist, any restriction
or condition upon the transfer, voting or control of any Pledged Equity.

                                   ARTICLE IV.

                       Remedies, Powers and Authorization

         Section 4.1. Provisions Concerning the Collateral.

         (a) Additional Financing Statement Filings. Pledgor hereby authorizes
Pledgee to file, without the signature of Pledgor where permitted by law, one
(1) or more financing or continuation statements, and amendments thereto,
relating to the Collateral. Pledgor further agrees that a carbon, photographic
or other reproduction of this Agreement or any financing statement describing
any Collateral is sufficient as a financing statement and may be filed in any
jurisdiction Pledgee may deem appropriate.

         (b) Power of Attorney. Pledgor hereby irrevocably appoints Pledgee as
Pledgor's attorney-in-fact and proxy, with full authority in the place and stead
of Pledgor and in the name of Pledgor or otherwise, from time to time in
Pledgee's discretion, to take any action (except for the exercise of any voting
rights pertaining to the Pledged Equity or any part thereof) and to execute any
instrument, certificate or notice which Pledgee may deem necessary or advisable
to accomplish the purposes of this Agreement including, without limitation: (i)
to request or instruct Pledgor (and each registrar, transfer agent, or similar
Person acting on behalf of Pledgor) to register the pledge or transfer of the
Collateral to Pledgee; (ii) to otherwise give notification to Pledgor,
registrar, transfer agent, financial intermediary, or other Person of Pledgee's
security interests hereunder; (iii) to ask, demand, collect, sue for, recover,
compound, receive and give acquittance and receipts for moneys due and to become
due under or in respect of any of the Collateral; (iv) to receive, indorse and
collect any drafts or other instruments, documents and chattel paper; and (v) to
file any claims or take any action or institute any proceedings which Pledgee
may deem necessary or desirable for the collection of any of the Collateral or
otherwise to enforce the rights of Pledgee with respect to any of the
Collateral.

         (c) Performance by Pledgee. If Pledgor fails to perform any agreement
or obligation contained herein, Pledgee may itself perform, or cause performance
of, such agreement or obligation, and the expenses of Pledgee incurred in
connection therewith shall be payable by Pledgor under Section 4.4.

                                       7
<PAGE>   8

         (d) Collection Rights. Pledgee shall have the right at any time, upon
the occurrence and during the continuance of an Event of Default, to notify any
or all obligors (including without limitation Pledgor) under any accounts or
general intangibles included among the Collateral of the assignment thereof to
Pledgee and to direct such obligors to make payment of all amounts due or to
become due to Pledgor thereunder directly to Pledgee and, upon such notification
and at the expense of Pledgor and to the extent permitted by law, to enforce
collection thereof and to adjust, settle or compromise the amount or payment
thereof, in the same manner and to the same extent as Pledgor could have done.
After Pledgor receives notice that Pledgee has given any notice referred to
above in this subsection, (i) all amounts and proceeds (including instruments
and writings) received by Pledgor in respect of such accounts or general
intangibles shall be received in trust for the benefit of Pledgee hereunder,
shall be segregated from other funds of Pledgor and shall be forthwith paid over
to Pledgee in the same form as so received (with any necessary indorsement) to
be held as cash collateral and (A) released to Pledgor upon the remedy of all
Defaults or Events of Default, or (B) if any Event of Default shall have
occurred and be continuing, applied as specified in Section 4.3, and (ii)
Pledgor will not adjust, settle or compromise the amount or payment of any such
account or general intangible or release wholly or partly any account debtor or
obligor thereof (including without limitation Pledgor) or allow any credit or
discount thereon.

         Section 4.2. Event of Default Remedies. If an Event of Default shall
have occurred and be continuing, Pledgee may from time to time in its
discretion, without limitation and without notice except as expressly provided
below:

         (a) exercise in respect of the Collateral, in addition to other rights
and remedies provided for herein, under the other Obligation Documents or
otherwise available to it, all the rights and remedies of a secured party on
default under the Code (whether or not the Code applies to the affected
Collateral);

         (b) require Pledgor to, and Pledgor hereby agrees that it will at its
expense and upon request of Pledgee forthwith, assemble all or part of the
Collateral as directed by Pledgee and make it available to Pledgee at a place to
be designated by Pledgee which is reasonably convenient to both parties;

         (c) reduce its claim to judgment against Pledgor or foreclose or
otherwise enforce, in whole or in part, the security interest created hereby by
any available judicial procedure;

         (d) dispose of, at its office, on the premises of Pledgor or elsewhere,
all or any part of the Collateral, as a unit or in parcels, by public or private
proceedings, and by way of one or more contracts (it being agreed that the sale
of any part of the Collateral shall not exhaust Pledgee's power of sale, but
sales may be made from time to time, and at any time, until all of the
Collateral has been sold or until the Obligations have been paid and performed
in full), and at any such sale it shall not be necessary to exhibit any of the
Collateral;

         (e) buy (or allow any Bank to buy) the Collateral, or any part thereof,
at any public sale;

                                       8
<PAGE>   9

         (f) buy (or allow any Bank to buy) the Collateral, or any part thereof,
at any private sale if the Collateral is of a type customarily sold in a
recognized market or is of a type which is the subject of widely distributed
standard price quotations;

         (g) apply by appropriate judicial proceedings for appointment of a
receiver for the Collateral, or any part thereof, and Pledgor hereby consents to
any such appointment; and

         (h) at its discretion, retain the Collateral in satisfaction of the
Obligations whenever the circumstances are such that Pledgee is entitled to do
so under the Code or otherwise (provided that Pledgee shall in no circumstances
be deemed to have retained the Collateral in satisfaction of the Obligations in
the absence of an express notice by Pledgee to Pledgor that Pledgee has either
done so or intends to do so).

         Pledgor agrees that, to the extent notice of sale shall be required by
law, at least five (5) days' notice to Pledgor of the time and place of any
public sale or the time after which any private sale is to be made shall
constitute reasonable notification. Pledgee shall not be obligated to make any
sale of Collateral regardless of notice of sale having been given. Pledgee may
adjourn any public or private sale from time to time by announcement at the time
and place fixed therefor, and such sale may, without further notice, be made at
the time and place to which it was so adjourned.

         Section 4.3. Application of Proceeds. If any Event of Default shall
have occurred and be continuing, Pledgee may in its discretion apply any cash
held by Pledgee as Collateral, and any cash proceeds received by Pledgee in
respect of any sale of, collection from, or other realization upon all or any
part of the Collateral, to any or all of the following in such order as Pledgee
may elect:

         (a) to the repayment of the reasonable costs and expenses, including
reasonable attorneys' fees and legal expenses, incurred by Pledgee in connection
with (i) the administration of this Agreement, (ii) the custody, preservation,
use or operation of, or the sale of, collection from, or other realization upon,
any Collateral, (iii) the exercise or enforcement of any of the rights of
Pledgee hereunder, or (iv) the failure of Pledgor to perform or observe any of
the provisions hereof;

         (b) to the payment or other satisfaction of any Liens, encumbrances, or
adverse claims upon or against any of the Collateral;

         (c) to the reimbursement of Pledgee for the amount of any obligations
of Pledgor or any Other Liable Party paid or discharged by Pledgee pursuant to
the provisions of this Agreement or the other Obligation Documents, and of any
expenses of Pledgee payable by Pledgor hereunder or under the other Obligation
Documents;

         (d) to the satisfaction of any other Obligations or any other
indebtedness of Pledgor and/or Borrower to Banks or Pledgee;

         (e) by holding the same as Collateral;

                                       9
<PAGE>   10

         (f) To the payment of any other amounts required by applicable law
(including, without limitation, Section 9.504(a)(3) of the Code or any successor
or similar, applicable statutory provision); and

         (g) by delivery to Pledgor or to whomsoever shall be lawfully entitled
to receive the same or as a court of competent jurisdiction shall direct.

         Section 4.4. Release and Expenses. In addition to, and not in
qualification of, any similar obligations under other Obligation Documents:

         (a) Pledgor agrees to release and forever discharge Pledgee and each
Bank from and against any and all claims, losses and liabilities growing out of
or resulting from this Agreement (including, without limitation, enforcement of
this Agreement). The foregoing release and discharge shall apply whether or not
such claims, losses and liabilities are in any way or to any extent owed, in
whole or in part, under any claim or theory of strict liability or are, to any
extent caused, in whole or in part, by any negligent act or omission of any kind
by Pledgee or any Bank.

         (b) Pledgor will upon demand pay to Pledgee the amount of any and all
costs and expenses, including the fees and disbursements of Pledgee's counsel
and of any experts and agents, which Pledgee may incur in connection with (i)
the transactions which give rise to this Agreement; (ii) the preparation of this
Agreement and the perfection and preservation of the security interest created
under this Agreement; (iii) the administration of this Agreement; (iv) the
custody, preservation, use or operation of, or the sale of, collection from, or
other realization upon, any Collateral; (v) the exercise or enforcement of any
of the rights of Pledgee hereunder; or (vi) the failure by Pledgor to perform or
observe any of the provisions hereof, except expenses resulting from Pledgee's
gross negligence or willful misconduct.

         Section 4.5. Non-Judicial Remedies. In granting to Pledgee the power to
enforce its rights hereunder without prior judicial process or judicial hearing,
Pledgor expressly waives, renounces and knowingly relinquishes any legal right
which might otherwise require Pledgee to enforce its rights by judicial process.
In so providing for non judicial remedies, Pledgor recognizes and concedes that
such remedies are consistent with the usage of trade, are responsive to
commercial necessity, and are the result of a bargain at arm's length. Nothing
herein is intended to prevent Pledgee or Pledgor from resorting to judicial
process at either party's option.

         Section 4.6. Other Recourse. Pledgor waives any right to require
Pledgee or Banks to proceed against any other Person, exhaust any Collateral or
other security for the Obligations, or to have any Other Liable Party joined
with Pledgor in any suit arising out of the Obligations or this Agreement, or
pursue any other remedy in Pledgee's power. Pledgor further waives any and all
notice of acceptance of this Agreement and of the creation, modification,
rearrangement, renewal or extension for any period of any of the Obligations of
any Other Liable Party from time to time. Pledgor further waives any defense
arising by reason of any disability or other defense of any Other Liable Party
or by reason of the cessation from any cause whatsoever of the liability of any
Other Liable Party. Until all of the Obligations shall have been paid in full,
Pledgor shall have no right to subrogation and Pledgor waives the right to
enforce any remedy which Pledgee or any Bank has or may hereafter have against
any Other Liable Party, and waives any benefit of and any right to participate
in any other security whatsoever now or hereafter held by Pledgee. Pledgor
authorizes Pledgee and each Bank, without notice or demand

                                       10
<PAGE>   11

and without any reservation of rights against Pledgor and without affecting
Pledgor's or Borrower's liability hereunder or on the Obligations, from time to
time to (a) take or hold any other property of any type from any other Person as
security for the Obligations, and exchange, enforce, waive and release any or
all of such other property, (b) apply the Collateral or such other property and
direct the order or manner of sale thereof as Pledgee may in its discretion
determine, (c) renew, extend for any period, accelerate, modify, compromise,
settle or release any of the obligations of any Other Liable Party in respect to
any or all of the Obligations or other security for the Obligations, (d) waive,
enforce, modify, amend or supplement any of the provisions of any Obligation
Document with any Person other than Pledgor, and (e) release or substitute any
Other Liable Party.

         Section 4.7. Voting Rights. Dividends Etc, in Respect of Pledged Equity

         (a) So long as no Event of Default shall have occurred and be
continuing Pledgor may receive and retain any and all dividends or interest paid
in respect of the Pledged Equity; provided, however, that any and all

                  (i) dividends and interest paid or payable other than in cash
         in respect of, and instruments and other property received, receivable
         or otherwise distributed in respect of or in exchange for, any Pledged
         Equity,

                  (ii) dividends and other distributions paid or payable in cash
         in respect of any Pledged Equity in connection with a partial or total
         liquidation or dissolution or in connection with a reduction of
         capital, capital surplus or paid-in surplus, and

                  (iii) cash paid, payable or otherwise distributed in
         redemption of, or in exchange for, any Pledged Equity, shall be, and
         shall forthwith be delivered to Pledgee to hold as, Pledged Equity and
         shall, if received by Pledgor, be received in trust for the benefit of
         Pledgee, be segregated from the other property or funds of Pledgor, and
         be forthwith delivered to Pledgee in the exact form received with any
         necessary indorsement or appropriate stock powers duly executed in
         blank, to be held by Pledgee as Collateral.

         (b) Upon the occurrence and during the continuance of an Event of
Default:

                  (i) all rights of Pledgor to receive and retain the dividends
         and interest payments which Pledgor would otherwise be authorized to
         receive and retain pursuant to subsection (a) of this section shall
         automatically cease, and all such rights shall thereupon become vested
         in Pledgee which shall thereupon have the right to receive and hold as
         Pledged Equity such dividends and interest payments;

                  (ii) without limiting the generality of the foregoing, Pledgee
         may at its option exercise any and all rights of conversion, exchange,
         subscription or any other rights, privileges or options pertaining to
         any of the Pledged Equity (except voting rights) as if it were the
         absolute owner thereof, including, without limitation, the right to
         exchange, in its discretion, any and all of the Pledged Equity upon the
         merger, consolidation, reorganization, recapitalization or other
         adjustment of Pledgor or any of its Subsidiaries, or upon the exercise
         by Pledgor or any of its Subsidiaries of any right, privilege or option
         pertaining to any Pledged Equity, and, in connection therewith, to
         deposit and deliver any

                                       11
<PAGE>   12

         and all of the Pledged Equity with any committee, depository, transfer
         agent, registrar or other designated agent upon such terms and
         conditions as it may determine; and

                  (iii) all dividends and interest payments which are received
         by Pledgor contrary to the provisions of subsection (b) (i) of this
         section shall be received in trust for the benefit of Pledgee, shall be
         segregated from other funds of Pledgor, and shall be forthwith paid
         over to Pledgee as Pledged Equity in the exact form received, to be
         held by Pledgee as Collateral.

Anything herein to the contrary notwithstanding, Pledgee may not exercise any
voting rights pertaining to the Pledged Equity and Pledgor may at all times
exercise any and all voting rights pertaining to the Pledged Equity or any part
thereof for any purpose not inconsistent with the terms of this Agreement or any
other Obligation Document; provided, however, upon the occurrence and during the
continuance of a Default or an Event of Default, Pledgor will not exercise or
refrain from exercising any such right, as the case may be, if Pledgee gives
notice that, in Pledgee's judgment, such action would result in a Material
Adverse Change with respect to the value of the Pledged Equity or the benefits
to Pledgee of its security interest hereunder.

         Section 4.8. Private Sale of Pledged Equity. Pledgor recognizes that
Pledgee may deem it impracticable to effect a public sale of all or any part of
the Pledged Equity and that Pledgee may, therefore, determine to make one or
more private sales of any such securities to a restricted group of purchasers
who will be obligated to agree, among other things, to acquire such securities
for their own account, for investment and not with a view to the distribution or
resale thereof. Pledgor acknowledges that any such private sale may be at prices
and on terms less favorable to the seller than the prices and other terms which
might have been obtained at a public sale and, notwithstanding the foregoing,
agrees that such private sales shall be deemed to have been made in a
commercially reasonable manner and that Pledgee shall have no obligation to
delay the sale of any such securities for the period of time necessary to permit
Pledgor to register such securities (with no obligation of Pledgor to accomplish
such registration) for public sale under the Securities Act of 1933, as amended.
Pledgor further acknowledges and agrees that any offer to sell such securities
which has been (a) publicly advertised on a bona fide basis in a newspaper or
other publication of general circulation in the financial community of Dallas,
Texas (to the extent that such an offer may be so advertised without prior
registration under the Securities Act), or (b) made privately in the manner
described above to not less than fifteen (15) bona fide offerees shall be deemed
to involve a "public sale" for the purposes of Section 9.504(c) of the Code (or
any successor or similar, applicable statutory provision) as then in effect in
the State of Texas, notwithstanding that such sale may not constitute a "public
offering" under the Securities Act of 1933, as amended, and that Pledgee may, in
such event, bid for the purchase of such securities.

                                    ARTICLE V

                                  Miscellaneous

         Section 5.1. Notices. Any notice or communication required or permitted
hereunder shall be given in writing, sent by personal delivery, by telecopy, by
delivery service with proof of delivery, or by registered or certified United
States mail, postage prepaid, addressed to the appropriate party as follows:

                                       12
<PAGE>   13

To Pledgor:                Encore Acquisition Partners, Inc.
                           201 Main Street, Suite 1455
                           Fort Worth, Texas 76102
                           Fax No.: (817) 877-1655

To Pledgee:                NationsBank, N.A., as Administrative Agent for Banks
                           901 Main Street, 64th Floor
                           Dallas, Texas 75202
                           Fax No. (214) 209-1285

or to such other address or to the attention of such other individual as
hereafter shall be designated in writing by the applicable party sent in
accordance herewith. Any such notice or communication shall be deemed to have
been given (a) in the case of personal delivery or delivery service, as of the
date of first attempted delivery at the address or in the manner provided
herein, (b) in the case of telecopy, upon receipt, or (c) in the case of
registered or certified United States mail, three (3) days after deposit in the
mail.

         Section 5.2. Amendments. No amendment of any provision of this
Agreement shall be effective unless it is in writing and signed by Pledgor,
Pledgee and Banks, and no waiver of any provision of this Agreement, and no
consent to any departure by Pledgor therefrom, shall be effective unless it is
in writing and signed by Pledgee and Banks, and then such waiver or consent
shall be effective only in the specific instance and for the specific purpose
for which given and to the extent specified in such writing.

         Section 5.3. Preservation of Rights. No failure on the part of Pledgee
or any Bank to exercise, and no delay in exercising, any right hereunder or
under any other Obligation Document shall operate as a waiver thereof; nor shall
any single or partial exercise of any such right preclude any other or further
exercise thereof or the exercise of any other right. Neither the execution nor
the delivery of this Agreement shall in any manner impair or affect any other
security for the Obligations. The rights and remedies of Pledgee and Banks
provided herein and in the other Obligation Documents are cumulative of and are
in addition to, and not exclusive of, any rights or remedies provided by law.
The rights of Pledgee and Banks under any Obligation Document against any party
thereto are not conditional or contingent on any attempt by Pledgee or Banks to
exercise any of its rights under any other Obligation Document against such
party or against any other Person.

         Section 5.4. Unenforceability. Any provision of this Agreement which is
prohibited or unenforceable in any jurisdiction shall, as to such jurisdiction,
be ineffective to the extent of such prohibition or invalidity without
invalidating the remaining portions hereof or thereof or affecting the validity
or enforceability of such provision in any other jurisdiction.

         Section 5.5. Survival of Agreements. All representations and warranties
of Pledgor herein, and all covenants and agreements herein shall survive the
execution and delivery of this Agreement, the execution and delivery of any
other Obligation Documents and the creation of the Obligations.

                                       13
<PAGE>   14

         Section 5.6. Other Liable Party. Neither this Agreement nor the
exercise by Pledgee or any Bank or the failure of Pledgee or any Bank to
exercise any right, power or remedy conferred herein or by law shall be
construed as relieving any Other Liable Party from liability on the Obligations
or any deficiency thereon. This Agreement shall continue irrespective of the
fact that the liability of any Other Liable Party may have ceased or
irrespective of the validity or enforceability of any other Obligation Document
to which Pledgor or any Other Liable Party may be a party, and notwithstanding
the reorganization, death, incapacity or bankruptcy of any Other Liable Party,
and notwithstanding the reorganization or bankruptcy or other event or
proceeding affecting any Other Liable Party.

         Section 5.7. Binding Effect and Assignment. This Agreement creates a
continuing security interest in the Collateral and (a) shall be binding on
Pledgor and its successors and permitted assigns, and (b) shall inure, together
with all rights and remedies of Pledgee hereunder, to the benefit of Pledgee and
Banks and their respective successors, transferees and assigns. Without limiting
the generality of the foregoing, Pledgee and Banks may pledge, assign or
otherwise transfer any or all of their respective rights under any or all of the
Obligation Documents to any other Person, and such other Person shall thereupon
become vested with all of the benefits in respect thereof granted herein or
otherwise. None of the rights or duties of Pledgor hereunder may be assigned or
otherwise transferred without the prior written consent of Pledgee and Banks.

         Section 5.8. Termination. It is contemplated by the parties hereto that
there may be times when no Obligations are outstanding, but notwithstanding such
occurrences, this Agreement shall remain valid and shall be in full force and
effect as to subsequent outstanding Obligations. Upon the satisfaction in full
of the Obligations, upon the termination or expiration of the Credit Agreement
and any other Commitment of Banks to extend credit to Borrower, and upon written
request for the termination hereof delivered by Pledgor to Pledgee and Banks,
this Agreement and the security interest created hereby shall terminate and all
rights to the Collateral shall revert to Pledgor. Pledgee will, upon Pledgor's
request and at Pledgor's expense, (a) return to Pledgor such of the Collateral
as shall not have been sold or otherwise disposed of or applied pursuant to the
terms hereof, and (b) execute and deliver to Pledgor such documents as Pledgor
shall reasonably request to evidence such termination.

         SECTION 5.9. GOVERNING LAW. THIS AGREEMENT SHALL BE CONSTRUED IN
ACCORDANCE WITH AND GOVERNED BY THE LAWS OF THE STATE OF TEXAS AND THE LAWS OF
THE UNITED STATES OF AMERICA.

         Section 5.10. Counterparts. This Agreement may be separately executed
in any number of counterparts, all of which when so executed shall be deemed to
constitute one and the same Agreement.

         Section 5.11. Loan Paper. This Agreement is a "Loan Paper", as defined
in the Credit Agreement, and, except as expressly provided herein to the
contrary, this Agreement is subject to all provisions of the Credit Agreement
governing such Loan Paper.

                                       14
<PAGE>   15

         IN WITNESS WHEREOF, Pledgor has caused this Agreement to be executed
and delivered by its officer thereunto duly authorized, as of the date first
above written.

                                     ENCORE ACQUISITION PARTNERS, INC.,
                                     a Delaware corporation

                                     By: /s/ BRUCE B. SELKIRK, III
                                        ----------------------------------------
                                         Bruce B. Selkirk, III,
                                         Executive Vice President and
                                         Chief Financial Officer

                                       15

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