TO CREDIT AGREEMENT Dated as of May 28, 2004 AMONG

EXHIBIT 10.13

EXECUTION COPY

THIRD AMENDMENT

TO

CREDIT AGREEMENT

Dated as of May 28, 2004

AMONG

PLAINS EXPLORATION & PRODUCTION COMPANY,

AS BORROWER,

THE GUARANTORS,

JPMORGAN CHASE BANK,

AS ADMINISTRATIVE AGENT,

AND

THE LENDERS PARTY HERETO

THIRD AMENDMENT TO CREDIT AGREEMENT

THIS THIRD AMENDMENT TO CREDIT AGREEMENT (this “Third Amendment”) dated as of May 28, 2004, is among PLAINS EXPLORATION & PRODUCTION COMPANY, a Delaware corporation (the “Borrower”); each of the undersigned guarantors (the “Guarantors”, and together with the Borrower, the “Obligors”); JPMORGAN CHASE BANK, as administrative agent (in such capacity, together with its successors in such capacity, the “Administrative Agent”) for the lenders party to the Credit Agreement referred to below (collectively, the “Lenders”); and each of the undersigned Lenders.

R E C I T A L S

A. The Borrower, the Agents and the Lenders are parties to that certain Credit Agreement dated as of April 4, 2003 (as amended by the First Amendment to Credit Agreement dated as of August 8, 2003 and the Second Amendment to Credit Agreement dated as of May 14, 2004, the “Credit Agreement”), pursuant to which the Lenders have made certain credit available to and on behalf of the Borrower.

B. The Borrower has requested and the Lenders have agreed to amend certain provisions of the Credit Agreement.

C. NOW, THEREFORE, in consideration of the premises and the mutual covenants herein contained, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

Section 1. Defined Terms. Each capitalized term used herein but not otherwise defined herein has the meaning given such term in the Credit Agreement. Unless otherwise indicated, all section references in this Third Amendment refer to sections of the Credit Agreement.

Section 2. Amendments to Credit Agreement.

2.1 Amendments to Section 1.02.

(a) The definition of “Agreement” is hereby amended in its entirety to read follows:

“Agreement” means this Credit Agreement, as amended by the First Amendment, the Second Amendment and the Third Amendment, as the same may from time to time be amended, modified, supplemented or restated.

(b) The following definitions arc hereby added where alphabetically appropriate to read as follows:

“Senior Indenture” means the indenture among the Borrower, as issuer, any subsidiary guarantors party thereto and a trustee, pursuant to which Senior Notes are issued, as amended or supplemented pursuant to Section 9.04(b).

“Senior Notes” means senior unsecured notes issued by the Borrower pursuant to the Senior Indenture, in compliance with Section 9.02(i), having a stated coupon acceptable to the Administrative Agent, a final maturity no earlier than seven years from the Effective Date and other terms reasonably acceptable to the Administrative Agent.

“Third Amendment” means the Third Amendment to Credit Agreement dated as of May 28, 2004 among the Borrower, the Guarantors and the Lenders party thereto.

2.2 Amendment to Section 2.07(e). Section 2.07(e) is hereby amended by deleting the word “redeemed” and replacing it with the word “tendered” in the twenty-third line thereof.

2.3 Amendment to Section 7.03(c). Section 7.03(c) is hereby amended by inserting the words “or the Senior Indenture, as the case may be” after the words “Permitted Additional Senior Subordinated Indenture” in the third line thereof.

2.4 Amendment to Section 7.04(c). Section 7.04(c) is hereby amended by inserting the words “or Senior Notes, as the case may be” after the words “Permitted Additional Senior Subordinated Notes” in the second line thereof.

2.5 Amendment to Section 8.01(n). Section 8.01(n) is hereby amended by inserting the words “or Senior Notes” after the words “Permitted Additional Senior Subordinated Notes” in the title thereof and by inserting the words “or Senior Notes, as the case may be,” after the words “Permitted Additional Senior Subordinated Notes” in the second line thereof.

2.6 Amendment to 8.14(d). Section 8.14(d) is hereby amended by inserting the words “, the Senior Notes” after the words “the 2002 Senior Subordinated Notes” in the twelfth line thereof.

2.7 Amendment to Section 9.02(i). Section 9,02(i) is hereby amended in its entirety to read as follows:

“(i) Debt under the Permitted Additional Senior Subordinated Notes and/or the Senior Notes and any guarantees thereof by the Guarantors (including any Persons becoming Guarantors simultaneously with the incurrence of such Debt), the principal amount of which does not exceed $300,000,000 in the aggregate; provided that: (i) the proceeds (net of transaction fees and expenses) of the issuance of such Permitted Additional Senior Subordinated Notes and/or Senior Notes shall be used solely to repay in full the outstanding loans and other amounts payable under the Nuevo Credit Agreement and if any excess proceeds remain after giving effect to such repayment, subject to the other terms of this Agreement, such excess proceeds may be used to repay outstanding Debt of the Borrower, (ii) the conditions of Section 2.07(e)(i)(A) and (B) have been or shall be concurrently satisfied (or waived in accordance with Section 12.02 of the Credit Agreement) and (iii) at the time of incurring such Debt (A) no Default has occurred and is then continuing and (B) no Default would result from the incurrence of such Debt after giving effect to the incurrence of such Debt (and any concurrent repayment of Debt with the proceeds of such incurrence).”

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2.8 Amendment to Section 9.04(a)(vii). Section 9.04(a)(vii) is hereby amended in its entirety to read as follows:

“(vii) to the extent not permitted by clauses (i) to (vi) above, the Borrower may make Restricted Payments in respect of Equity Interests of the Borrower in an mount not to exceed $2,500,000 in the aggregate minus the aggregate principal amount of 2002 Senior Subordinated Notes, Permitted Additional Senior Subordinated Notes and Senior Notes Redeemed under Section 9.04(b)(i).”

2.9 Amendments to Section 9.04(b). Section 9.04(b) is hereby amended in its entirety to read as follows:

“(b) Repayment of Senior Subordinated Notes and Senior Unsecured Notes: Amendment of Indentures. The Borrower will not, and will not permit any Restricted Subsidiary to, prior to the Termination Date: (i) call, make or offer to make any optional or voluntary Redemption (whether in whole or in part) of the 2002 Senior Subordinated Notes, the Permitted Additional Senior Subordinated Notes or the Senior Notes, provided that the Borrower may Redeem 2002 Senior Subordinated Notes, Permitted Additional Senior Subordinated Notes or Senior Notes to the extent that it could make a Restricted Payment under
Section 9.04(a)(vii), (ii) amend, modify, waive or otherwise change, consent or agree to any amendment, modification, waiver or other change to, any of the terms of the 2002 Senior Subordinated Notes, the Permitted Additional Senior Subordinated Notes, the Senior Notes, the 2002 Senior Subordinated Indenture, the Permitted Additional Senior Subordinated Indenture or the Senior Indenture if (A) the effect thereof would be to shorten its maturity or average life or increase the amount of any payment of principal thereof or increase the rate or shorten any period for payment of interest thereon, (B) such action requires the payment of a consent fee (other than in connection with a consent solicitation solely to conform all or a portion of the covenants contained in the 2002 Senior Subordinated Indenture to the covenants contained in the Permitted Additional Senior Subordinated Indenture or the Senior Indenture, provided that such consent fee is acceptable to the Administrative Agent) or (c) the effect thereof would be to add any guarantor or surety, unless such guarantor or surety also guarantees the Indebtedness pursuant to the Guaranty Agreement and each of the Borrower and such guarantor or surety otherwise complies with Section 8.14(d), or (iii) designate any Debt (other than obligations of the Borrower and the Restricted Subsidiaries pursuant to the Loan Documents) as “Designated Senior Indebtedness” or “Designated Guarantor Senior Indebtedness” or give any such other Debt any other similar designation for the purposes of the 2002 Senior Subordinated Indenture or the Permitted Additional Senior Subordinated Indenture.”

Section 3. Conditions Precedent. This Third Amendment shall not become effective until the date on which each of the following conditions is satisfied (or waived in accordance with Section 12.02 of the Credit Agreement) (the “Effective Date”):

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3.1 The Administrative Agent and the Lenders shall have received all fees and other amounts due and payable, if any, in connection with this Third Amendment on or prior to the Effective Date.

3.2 The Administrative Agent shall have received from all of the Lenders the Borrower and each Guarantor, counterparts (in such number as may be requested by the Administrative Agent) of this Third Amendment signed on behalf of such Persons.

3.3 The Administrative Agent shall have received such other documents as the Administrative Agent or special counsel to the Administrative Agent may reasonably request.

3.4 No Default shall have occurred and be continuing, after giving effect to the terms of this Third Amendment.

Section 4. Miscellaneous.

4.1 Confirmation. The provisions of the Credit Agreement, as amended by this Third Amendment, shall remain in full force and effect following the effectiveness of this Third Amendment.

4.2 Ratification and Affirmation: Representations and Warranties. Each Obligor hereby (a) acknowledges the terms of this Third Amendment; (b) ratifies and affirms its obligations under, and acknowledges, renews and extends its continued liability under, each Loan Document to which it is a party and agrees that each Loan Document to which it is a party remains in full force and effect, except as expressly amended hereby, notwithstanding the amendments contained herein and (c) represents and warrants to the Lenders that as of the date hereof, after giving effect to the terms of this Third Amendment: (i) all of the representations and warranties contained in each Loan Document to which it is a party are true and correct, except to the extent any such representations and warranties are expressly limited to an earlier date, in which case, such representations and warranties shall continue to be true and correct as of such specified earlier date, (ii) no Default has occurred and is continuing and (iii) since April 4, 2003, there has been no event, development or circumstance that has had or could reasonably be expected to have a Material Adverse Effect.

4.3 Loan Document. This Third Amendment is a “Loan Document” as defined and described in the Credit Agreement and all of the terms and provisions of the Credit Agreement relating to Loan Documents shall apply hereto.

4.4 Counterparts. This Third Amendment may be executed by one or more of the parties hereto in any number of separate counterparts, and all of such counterparts taken together shall be deemed to constitute one and the same instrument. Delivery of this Third Amendment by facsimile transmission shall be effective as delivery of a manually executed counterpart hereof.

4.5 No Oral Agreement. This Third Amendment, the Credit Agreement and the other Loan Documents executed in connection herewith and therewith represent the final agreement between the parties and may not be contradicted by evidence of prior, contemporaneous, or

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unwritten oral agreements of the parties. There are no subsequent oral agreements between the parties.

4.6 GOVERNING LAW. THIS THIRD AMENDMENT (INCLUDING, BUT NOT LIMITED TO, THE VALIDITY AND ENFORCEABILITY HEREOF) SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

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IN WITNESS WHEREOF, the pasties hereto have caused this Third Amendment to be duly executed as of the date first written above.

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