Exhibit 3.4

Delaware

The First State

I, HARRIET SMITH WINDSOR, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO HEREBY CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF AMENDMENT OF “BRIGHAM EXPLORATION COMPANY”, FILED IN THIS OFFICE ON THE SIXTEENTH DAY OF JUNE, A.D. 2006, AT 12:12 O’CLOCK P.M.

A FILED COPY OF THIS CERTIFICATE HAS BEEN FORWARDED TO THE NEW CASTLE COUNTY RECORDER OF DEEDS.

2721671 8100	(SEAL)	/s/ Harriet Smith Windsor
060582898		Harriet Smith Windsor, Secretary of State
		AUTHENTICATION: 4834727
		DATE: 06-16-06

State of Delaware

Secretary of State

Division of Corporations

Delivered 12:44 PM 06/16/2006

FILED 12:12 PM 06/16/2006

SRV 060582898 — 2721671 FILE

CERTIFICATE OF AMENDMENT
OF
CERTIFICATE OF INCORPORATION
OF
BRIGHAM EXPLORATION COMPANY

Brigham Exploration Company, a corporation organized and existing under and by virtue of the Delaware General Corporation Law (the “Corporation”).

DOES HEREBY CERTIFY:

FIRST: That the Board of Directors of the Corporation has approved the adoption of resolutions setting forth a proposed amendment to the Certificate of Incorporation of the Corporation, declaring said amendment to be advisable and directing that said amendment be considered by the stockholders of the Corporation entitled to vote thereon. The resolution setting forth the proposed amendment is as follows:

RESOLVED FURTHER, that, subject to stockholder approval of the Amendment, the first paragraph of the Article numbered “Fourth” of the Certificate of Incorporation of the Company be amended and restated to read in its entirety as follows (with the remainder of Fourth Article to remain unchanged):

“FOURTH: The total number of shares of all classes of stock which the Company shall have authority to issue is 100,000,000 shares, consisting solely of 10,000,000 shares of Preferred Stock, par value $.01 per share (the “Preferred Stock”), and 90,000,000 shares of Common Stock, par value $.01per share (the “Common Stock”)”.

RESOLVED FURTHER, that subject to stockholder approval of the Amendment, the proper officers of the Company are hereby authorized and directed to execute a Certificate of Amendment reflecting the Amendment and to file the Certificate of Amendment with the Secretary of State of Delaware.

SECOND: That during the June 1, 2006 annual meeting of the stockholders, the stockholders of theCompany voted to approve the amendment.

THIRD: That said amendment was duly adopted in accordance with the provisions of Section 242 of the Delaware General Corporation Law.

IN WITNESS WHEREOF, Brigham Exploration Company has caused this certificate to be signed by its duly authorized officer on this 14^th day of June, 2006.

BRIGHAM EXPLORATION COMPANY
By:	/s/ Ben M. Brigham
	Ben M. Brigham
	Chairman of the Board, President & Chief Executive Officer