Exhibit 10.4

FIRST AMENDMENT TO PLEDGE AGREEMENT

This FIRST AMENDMENT TO PLEDGE AGREEMENT, dated as of November [  ], 2007 (this “Amendment”), is by and between JPMORGAN CHASE BANK, N.A., solely in its capacity as trustee for MESA OFFSHORE TRUST, a trust formed under the laws of the State of Texas, having an address at 919 Congress Avenue, Austin, Texas 78701 (“Pledgor”) and JPMORGAN CHASE BANK, N.A., having an address at 1111 Polaris Parkway, Columbus, Ohio 43240 (“Secured Party”).

RECITALS

A.            Pledgor and Secured Party (collectively, the “Parties”) entered into the Pledge Agreement, dated as of September 28, 2007 (the “Original Pledge Agreement”; capitalized terms used but not defined in this Amendment have the meanings ascribed to them in the Original Pledge Agreement, as amended hereby).

B.            The Parties entered into an Amended and Restated Promissory Note (the “Note”), dated November [  ], 2007, that amends, restates, renews and extends the Demand Promissory Note (the “Original Note”), dated September 28, 2007, executed by Pledgor to the order of Secured Party.

C.            The Parties wish to provide for the amendment of certain provisions of the Original Pledge Agreement, all on the terms and conditions set forth in this Amendment.

NOW, THEREFORE, in consideration of the premises set forth above, and for other good and valuable consideration, the receipt and adequacy of which are hereby acknowledged, the Parties hereto hereby agree as follows:

1.1          AMENDMENT

1.1.1        Certain Provisions.  The Parties hereby agree to amend the Original Pledge Agreement as follows:

(a)           As used in the Original Pledge Agreement, as amended hereby, the term “Note” shall have the meaning given to such term in Recital B of this Amendment.

(b)           The definition of “Collateral” in Section 1.1 (b) of the Original Pledge Agreement is hereby deleted in its entirety and replaced with the following:

“All assets that constitute the Trust Estate (as defined in the Indenture), including, but not limited to the following:

(a)           all of the issued and outstanding general partnership interests now or hereafter owned by Pledgor in the Partnership, together with any cash or property received in exchange or in substitution for such interests (the aforesaid general partnership interests and any income, proceeds, cash or other property received in

exchange or in substitution therefor is hereinafter referred to as the “Pledged Interests”); all distributions which may be made on, or distributed in consequence of the ownership of, the Pledged Interests; and all investment property, financial assets, securities, securities entitlements, instruments or distributions of any kind issuable, issued or received upon conversion of, in respect of, or in exchange for the Pledged Interests;

(b)           all investment property, financial assets, securities, securities entitlements, equity interests, subscriptions, warrants, options or other rights issued by the Partnership, if any, which are now or hereafter owned by Pledgor (the“Additional Collateral”);

(c)           all deposit accounts, together with all of Pledgor’s right, title, and interest in and to all sums of property (including cash equivalents and other investments) now or at any time hereafter on deposit therein, credited thereto or payable thereon, and all instruments, documents, and other writing evidencing such deposit accounts;

(d)           any consideration received or due to Pledgor, including any settlement, resolution or judgment obtained by or for the benefit of Pledgor, arising from or related to any claims or choses in action owned by Pledgor, including claims that arise from or relate to the Partnership, the assets of the Partnership, or the Pledged Interests; and

(e)           all proceeds of any and all of the foregoing.

In the event subscriptions, warrants, options, or other rights are issued or provided to Pledgor in connection with any of the Collateral, such subscriptions, warrants, options, and rights shall be deemed to be part of the Collateral.”

(c)           The reference in Section 3.3(b) of the Original Pledge Agreement to “Other Collateral” is hereby deleted in its entirety  and replaced with the term “Additional Collateral”, as such term is defined in Section 1.1.1(b)(b) of this Amendment

(d)           Section 6.1 of the Original Pledge Agreement is hereby deleted in its entirety and replaced with the following:

“In addition to any other rights accorded to Secured Party hereunder, upon the occurrence and during the continuance of any Event of Default or the maturity of the Note has occurred by acceleration or otherwise:”

1.2          MISCELLANEOUS

1.2.1        Headings Descriptive.  The headings of the several sections and subsections of this Amendment are inserted for convenience only and shall not in any way affect the meaning or construction of any provision of this Amendment.

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1.2.2        Counterparts.  This Amendment may be executed in any number of counterparts and by the different parties hereto on separate counterparts, each of which when so executed and delivered shall be an original, but all of which shall together constitute one and the same instrument.

1.2.3        Effect of Amendment.  The Original Pledge Agreement, as modified by this Amendment, is hereby ratified and confirmed by Pledgor and Secured Party in all respects and constitutes the legal, valid and binding obligation of the Parties, enforceable against the Parties in accordance with its terms.

1.2.4        Governing Law.  THIS AMENDMENT SHALL BE GOVERNED BY, AND CONSTRUED AND INTERPRETED IN ACCORDANCE WITH THE LAWS OF THE STATE OF TEXAS.

[Signature pages follow]

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