Exhibit 3.3

CERTIFICATE OF AMENDMENT

TO

CERTIFICATE OF DESIGNATION

OF

10% SENIOR REDEEMABLE CONVERTIBLE PREFERRED STOCK

OF

DUNE ENERGY, INC.

Dune Energy, Inc., a corporation organized and existing under the laws of the State of Delaware (the “Company”), DOES HEREBY CERTIFY as follows:

FIRST: That the exchange offer through which the holders of at least 95% of the aggregate principal amount of the Company’s 10- ¹/2% Senior Secured Notes due 2012 (the “Notes”) have exchanged their Notes for other securities of the Company, including shares of the Company’s common stock, par value $0.001 per share, in a transaction that is consistent with the terms and conditions set forth in the term sheet attached to the restructuring support and lockup letter agreement entered into among the Company and the holders of at least 75% in aggregate principal amount of the Notes, has been consummated;

SECOND: That the Board of Directors of the Company, through a written consent, duly adopted resolutions approving and adopting the amendments set forth below to the Certificate of Designation of 10% Senior Redeemable Convertible Preferred Stock of the Company (the “Certificate of Designation”), and that such amendments have been approved and adopted by the requisite number of existing holders of the Company’s common stock, par value $0.001 per share, and the Company’s 10% Senior Redeemable Convertible Preferred Stock, par value $0.001 per share.

THIRD: That the amendments set forth below have been duly adopted in accordance with the applicable provisions of Section 242 of the General Corporation Law of the State of Delaware.

FOURTH: That the Certificate of Designation is hereby amended as follows:

“Unless a greater percentage shall then be required by law, the rights of Holders of Redeemable Convertible Preferred Stock to have the Company redeem such securities upon the occurrence of certain conditions detailed in Section 12 herein (or any rights deemed to have been granted and to continue to exist under either section once such section has been deleted or removed through a Certificate of Amendment to this Certificate of Designation) may be waived by the affirmative vote or consent of the Holders of a majority of the then-outstanding Redeemable Convertible Preferred Stock. Any such waiver by the Holders of a majority of the then-outstanding Redeemable Convertible Preferred Stock that was signed prior to the date of the Certificate of Amendment to the Certificate of Designation by which this provision of Section 5(a)(vi) has been added to this Certificate of Designation shall be deemed effective and valid at the time such Certificate of Amendment is filed with the Secretary of State of the State of Delaware (the “Effective Time”).”

“(7) Mandatory Conversion

At the Effective Time, each share of Redeemable Convertible Preferred Stock shall automatically convert into 355.16037 shares of Common Stock and $24.31 in cash without any further action on the part of the Holders of such Redeemable Convertible Preferred Stock. The shares of Common Stock and cash shall be allocated to the beneficial holders of the Redeemable Convertible Preferred Stock in accordance with the number of shares of Redeemable Convertible Preferred Stock held by such holders, with fractional shares of Common Stock rounded up to the nearest whole share of Common Stock. The Company shall, as soon as possible thereafter, issue, and shall instruct the Transfer Agent to register, the number of shares of Common Stock to which each such Holder shall be entitled as a result of the conversion and to cancel all outstanding shares of Redeemable Convertible Preferred Stock, whether held in certificated or book-entry form. At the Effective Time, the Company shall no longer be required (i) to make any payment or allowance for unpaid dividends, whether or not in arrears, on the Redeemable Convertible Preferred Stock then outstanding or for dividends on the shares of Common Stock issued upon such conversion or (ii) to redeem the Redeemable Convertible Preferred Stock, and any right or claim to such dividends under the Redeemable Convertible Preferred Stock or the Common Stock issued upon such conversion or to the redemption price for the Redeemable Convertible Preferred Stock shall be cancelled and waived by the Holders of the Redeemable Convertible Preferred Stock who might otherwise be due such payments if and when declared by the Company or who might otherwise possess such rights to require the Company to redeem such Holders’ shares of Redeemable Convertible Preferred Stock, respectively.”

2

“‘VOTING RIGHTS TRIGGERING EVENT’ means if dividends on the Redeemable Convertible Preferred Stock are in arrears and unpaid for two or more calendar years.”

3

IN WITNESS WHEREOF, the Company has caused this Certificate of Amendment to the Certificate of Designation to be executed by the undersigned as of this 22nd day of December, 2011.

Signature Page to Certificate of Amendment to

Certificate of Designation