FIRST SUPPLEMENTAL INDENTURE

Exhibit 4.1

FIRST SUPPLEMENTAL INDENTURE

First Supplemental Indenture, dated as of December 30, 2008 (this “Supplemental Indenture”), by and among Dune Energy, Inc., a Delaware corporation (the “Company”), the Guarantors (as defined below) and The Bank of New York Mellon, as Trustee (in such capacity, the “Trustee”) and Collateral Agent (in such capacity, the “Collateral Agent”) under the Indenture referenced below.

WITNESSETH

WHEREAS, the Company, the Guarantors listed therein (the “Guarantors”) and the Trustee have heretofore executed and delivered the Indenture, dated as of May 15, 2007 (the “Indenture”), providing for the issuance of 10  ¹/2% Senior Secured Notes due 2012 of the Company (the “Notes”);

WHEREAS, Section 9.01(4) of the Indenture provides, among other things, that from time to time the Company, the Guarantors and the Trustee without the consent of the Holders, may amend, modify or supplement the Indenture to make any change that would provide any additional rights or benefits to the Holders or that does not adversely affect the legal rights of any such Holder under the Indenture, the Notes, the Guarantees or the Collateral Agreements;

WHEREAS, the amendments contained herein (i) provide additional benefits to the Holders and (ii) do not adversely affect the legal rights of any such Holder under this Indenture;

WHEREAS, all things necessary to make this Supplemental Indenture a valid and legally binding agreement of each of the Company and the Guarantors have been done;

NOW THEREFORE, in consideration of the foregoing and for good and valuable consideration, the receipt of which is hereby acknowledged, each party hereto agrees as follows for the benefit of the other parties and for the equal and ratable benefit of the Holders:

SECTION 1. Capitalized Terms. Capitalized terms used herein without definition shall have the respective meanings assigned to them in the Indenture.

SECTION 2. Addition of New Provision. Section 4.10 of the Indenture is amended by inserting the following new paragraph immediately prior to Section 4.11 of the Indenture:

“Without limiting any of the foregoing provisions of this Section 4.10, the Company shall not, prior to June 2, 2013, redeem any of the Company’s 10% Senior Redeemable Convertible Preferred Stock pursuant to Section 9 of the Certificate of Designation that sets forth the terms thereof. Notwithstanding any

provision of this Indenture to the contrary, the covenant set forth in the immediately preceding sentence shall survive the termination, defeasance or discharge of this Indenture, and the repayment of the Notes, whether at stated maturity, upon redemption or acceleration or otherwise, until June 2, 2013, and such covenant shall be enforceable by the Trustee and the Holders in accordance with the terms of the Indenture, for so long as any Notes are issued and outstanding, and thereafter until such date, by the Trustee and any Persons who were Holders on the last date when any Notes were issued and outstanding.”

SECTION 3. Trustee. The Trustee makes no representations as to the validity or sufficiency of this Supplemental Indenture. The recitals and statements herein are deemed to be those of the Company and the Guarantors and not of the Trustee.

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IN WITNESS WHEREOF, the parties hereto have caused this First Supplemental Indenture to be duly executed, all as of the date first above written.