FIRST AMENDMENT TO CREDIT AGREEMENT

Exhibit 10.2

Execution Version

FIRST AMENDMENT TO CREDIT AGREEMENT

This FIRST AMENDMENT TO CREDIT AGREEMENT (this “Amendment”), dated as of April 4, 2007, is entered into by and among CONSTELLATION ENERGY PARTNERS LLC, a Delaware limited liability company (the “Borrower”) and the Lenders signatory hereto (the “Lenders”).

RECITALS

WHEREAS, the Borrower, the Lenders and The Royal Bank of Scotland plc, as Administrative Agent and a Lender, are party to that certain Credit Agreement dated as of October 31, 2006, (such Credit Agreement, as the same may from time to time be amended, modified, supplemented or restated, herein called the “Credit Agreement”). Terms used and not otherwise defined herein shall have the respective meanings assigned to such terms in the Credit Agreement, and the provisions of Section 1.03 of the Credit Agreement are incorporated herein by reference; and

WHEREAS, the Borrower and the Lenders have agreed, subject to the terms and conditions hereinafter set forth, to amend the Credit Agreement as set forth below.

NOW, THEREFORE, in consideration of the mutual covenants and agreements herein contained and for other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the parties hereto hereby agree as follows:

SECTION 1. Amendments to Credit Agreement. Pursuant to Section 12.02 of the Credit Agreement, the Credit Agreement is hereby amended as set forth below.

(a) Borrowing Base. From and after the date hereof and until the same may be redetermined in accordance with the Credit Agreement, the Borrowing Base shall be $105,000,000 (the “New Base Amount”). For the avoidance of doubt, the redetermination of the Borrowing Base contained in this Section 1(a) is the scheduled redetermination described in Section 2.07(b) of the Credit Agreement.

(b) Section 7.22 of the Credit Agreement is amended and restated in full to read as follows:

“Schedule 7.22, as of the date hereof, and after the date hereof, each report required to be delivered by the Borrower pursuant to Section 8.01(c), sets forth a true and complete list of all Swap Agreements of the Borrower and each of its Subsidiaries, the material terms thereof (including the type, term, effective date, termination date and notional amounts or volumes), the net marked-to-market value thereof, all credit support agreements relating thereto (including any margin required or supplied) and the counterparty to each such agreement.”

(c) Section 8.01(c)(iv) of the Credit Agreement is amended and restated in full to read as follows:

“(iv) setting forth as of the last Business Day of such calendar month or fiscal year, a true and complete list of all Swap Agreements of the Borrower and each of its Consolidated Subsidiaries, the material terms thereof (including the type, term, effective date, termination date and notional amounts or volumes), the net mark-to-market value therefor, any new credit support agreements relating thereto not listed on Schedule 7.22, any margin required or supplied under any credit support document, and the counterparty to each such agreement.”

(d) Section 8.13(a) of the Credit Agreement is amended and restated in full to read as follows:

“(a) In connection with each redetermination of the Borrowing Base, the Borrower shall review the Reserve Report and the list of current Mortgaged Properties to ascertain whether the Mortgaged Properties represent at least 85% of the total value of the Proved Developed Producing Reserves and Proved Developed Nonproducing Reserves evaluated in the most recently completed Reserve Report after giving effect to exploration and production activities, acquisitions, dispositions and production. In the event that the Mortgaged Properties do not represent at least 85% of such total value, then the Borrower shall, and shall cause its Subsidiaries to, grant to the Administrative Agent or its designee as security for the Obligations a first-priority Lien interest (provided the Excepted Liens of the type described in clauses (a) to (d) and (f) of the definition thereof may exist, but subject to the provisos at the end of such definition) on additional Oil and Gas Properties not already subject to a Lien of the Security Instruments such that after giving effect thereto, the Mortgaged Properties will represent at least 85% of such total value. All such Liens will be created and perfected by and in accordance with the provisions of deeds of trust, security agreements and financing statements or other Security Instruments, all in form and substance reasonably satisfactory to the Administrative Agent or its designee and in sufficient executed (and acknowledged where necessary or appropriate) counterparts for recording purposes. In order to comply with the foregoing, if any Subsidiary places a Lien on its Oil and Gas Properties and such Subsidiary is not a Guarantor, then it shall become a Guarantor and comply with Section 8.13(b).”

(e) Section 12.02(b) of the Credit Agreement is amended and restated in full to read as follows:

“(b) Neither this Agreement nor any provision hereof nor any Security Instrument securing the payment or performance of the Obligations hereunder, nor any provision thereof may be waived, amended or modified except pursuant to an agreement or agreements in writing entered into by the Borrower and the Required Lenders or by the Borrower and the Administrative Agent with the consent of the Required Lenders; provided that no such agreement shall (i)

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increase the Maximum Credit Amount of any Lender without the written consent of such Lender, (ii) increase the Borrowing Base without the written consent of each Lender, decrease or maintain the Borrowing Base without the consent of the Required Lenders, or modify in any manner Section 2.07 without the consent of each Lender, (iii) reduce the principal amount of any Loan or Letter of Credit Disbursement or reduce the rate of interest thereon, or reduce any fees payable hereunder, or reduce any other Obligations hereunder or under any other Loan Document, without the written consent of each Lender affected thereby, (iv) postpone the scheduled date of payment of the principal amount of any Loan or Letter of Credit Disbursement, or any interest thereon, or any fees payable hereunder, or any other Obligations hereunder or under any other Loan Document, or reduce the amount of, waive or excuse any such payment, or postpone or extend the Termination Date or the Maturity Date without the written consent of each Lender affected thereby, (v) change Section 4.01(b) or Section 4.01(c) in a manner that would alter the pro rata sharing of payments required thereby, without the written consent of each Lender, (vi) waive or amend Section 6.01, Section 10.02(c) or Section 8.13 or change the definition of the terms “Domestic Subsidiary”, “Foreign Subsidiary”, “Material Domestic Subsidiary” or “Subsidiary”, without the written consent of each Lender, (vii) release any Guarantor (except as set forth in the Guarantee Agreement), release all or substantially all of the collateral (other than as provided in Section 11.09), or reduce the percentage set forth in Section 8.13(a) to less than 85%, without the written consent of each Lender, or (viii) change any of the provisions of this Section 12.02(b) or the definition of “Required Lenders” or any other provision hereof specifying the number or percentage of Lenders required to waive, amend or modify any rights hereunder or under any other Loan Documents or make any determination or grant any consent hereunder or any other Loan Documents, without the written consent of each Lender; provided further that no such agreement shall amend, modify or otherwise affect the rights or duties of the Administrative Agent, any other Agent, or any Issuer hereunder or under any other Loan Document without the prior written consent of the Administrative Agent, such other Agent or such Issuer, as the case may be. Notwithstanding the foregoing, any supplement to Schedule 7.14 (Subsidiaries) shall be effective simply by delivering to the Administrative Agent a supplemental schedule clearly marked as such and, upon receipt, the Administrative Agent will promptly deliver a copy thereof to the Lenders.”

SECTION 2. Upfront Fees. In accordance with Section 3.04(d) of the Credit Agreement, the Borrower agrees to pay to the Administrative Agent, for the account of each Lender, an upfront fee in the amount of 0.25% of each such Lender’s Applicable Percentage of the difference between the New Base Amount and the Base Amount (as defined in the Credit Agreement).

SECTION 3. Representations and Warranties of Borrower. The Borrower represents and warrants to the Lenders that:

(a) The representations and warranties of the Borrower contained in the Credit Agreement, as amended by this Amendment, are true correct on and as of the date hereof as

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though made on and as of such date (other than any such representations or warranties that, by their terms, refer to a specific date, in which case such representations and warranties are true and correct as of such specific date). No event has occurred and is continuing, or would result from the effectiveness of this Amendment, that constitutes or would constitute a Default; and

(b) The provisions of the Mortgages will be effective to grant to the Administrative Agent, for the ratable benefit of the Lenders, legal, valid and enforceable mortgage liens on (i) all of the right, title and interest of the Borrower and its Subsidiaries in the mortgaged property to the extent described therein and (ii) at least 85% of the total value of the Proved Developed Producing Reserves and Proved Developed Nonproducing Reserves evaluated in the Initial Reserve Report. Once such Mortgages have been recorded in the appropriate recording office and all recording taxes have been paid with respect thereto, the Mortgages will constitute perfected first liens on, and security interest in, such mortgaged property, subject to Excepted Liens.

SECTION 4. Conditions to Effectiveness. This Amendment shall become effective as of the date first written above, and it shall be a condition to the effectiveness of this Amendment that:

(a) Execution of Counterparts. The Administrative Agent shall have received counterparts of this Amendment, duly executed and delivered on behalf of the Borrower and the Lenders.

(b) Payment of Fees and Expenses. The Borrower shall have paid (i) the fees described in Section 3.04(d) of the Credit Agreement and (ii) all reasonable expenses (including the reasonable fees and expenses of Pillsbury Winthrop Shaw Pittman LLP) incurred in connection with the preparation, negotiation and execution of this Amendment and other matters relating to the Loan Documents from and after the last invoice to the extent invoiced.

SECTION 5. Reference to and Effect on Loan Documents.

(a) On and after the effective date of this Amendment, each reference in the Credit Agreement to “this Agreement,” “hereunder,” “hereof,” “herein” or any other expression of like import referring to the Credit Agreement, and each reference in the other Loan Documents to “the Credit Agreement,” “thereunder,” “thereof,” “therein” or any other expression of like import referring to the Credit Agreement, shall mean and be a reference to the Credit Agreement as amended by this Amendment.

(b) Except as specifically amended or waived above, the Credit Agreement and the other Loan Documents shall remain in full force and effect and are hereby ratified and confirmed. Without limiting the generality of the foregoing, the Security Instruments and all of the Collateral described therein do and shall continue to secure the payment of all obligations stated to be secured thereby under the Credit Agreement, as amended hereby, and the other Loan Documents.

(c) Except as provided in Section 1, the execution, delivery and effectiveness of this Amendment shall not operate as a waiver of any right, power or remedy of the Lenders under any of the Loan Documents or constitute a waiver of any provision of any of the Loan Documents.

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SECTION 6. Execution in Counterparts. This Amendment may be executed in any number of counterparts and by the parties hereto in separate counterparts, each of which when so executed and delivered shall be deemed to be an original and all of which taken together shall constitute one and the same agreement.

SECTION 7. Governing Law. THIS AMENDMENT SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK WITHOUT REFERENCE TO THE CHOICE OF LAW PRINCIPLES THEREOF.

[Signature pages follow]

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The parties hereto have caused this Amendment to be executed by their respective duly authorized representatives as of the date first written above.

SIGNATURE PAGE 1

AMENDMENT

[RBS signature page to Amendment]

[BNP Paribas signature page to Amendment]

[Wachovia signature page to Amendment]

[Bank of Nova Scotia signature page to Amendment]

[UBS Loan Finance signature page to Amendment]

[Bank of Scotland signature page to Amendment]

[Societe Generale signature page to Amendment]