Exhibit 24

POWER OF ATTORNEY
For Executing Forms 3, 4 and 5

Know all by these presents, that the undersigned hereby constitutes and appoints each of Kari Potts, David Brigham and Eric Sigsbey, signing singly, as the undersigned’s true and lawful attorney-in-fact to:

(1)

execute for and on behalf of the undersigned, in the undersigned’s capacity as an officer and/or director of Brigham Exploration Company (the “Company”), Forms 3, 4 and 5 in accordance with Section 16(a) of the Securities Exchange Act of 1934, and the rules promulgated thereunder;

(2)

do and perform any and all acts for and on behalf of the undersigned which may be necessary or desirable to complete and execute any such Form 3, 4 or 5 and timely file such form with the United States Securities and Exchange Commission and any stock exchange or similar authority; and

(3)

take any other action of any type whatsoever in connection with the foregoing which, in the opinion of such attorney-in-fact, may be of benefit to, in the best interest of, or legally required by, the undersigned, it being understood that the documents executed by such attorney-in-fact on behalf of the undersigned pursuant to this Power of Attorney shall be in such form and shall contain such terms and conditions as such attorney-in-fact may approve in her or his discretion.

The undersigned hereby grants to each such attorney-in-fact full power and authority to do and perform any and every act and thing whatsoever requisite, necessary or proper to be done in the exercise of any of the rights and powers herein granted, as fully to all intents and purposes as the undersigned might or could do if personally present, with full power of substitution or revocation, hereby ratifying and confirming all that such attorney-in-fact, or her or his substitute or substitutes, shall lawfully do or cause to be done by virtue of this Power of Attorney and the rights and powers herein granted. The undersigned acknowledges that the foregoing attorneys-in-fact, in serving in such capacity at the request of the undersigned, are not assuming, nor is the Company assuming, any of the undersigned’s responsibilities to comply with Section 16 of the Securities Exchange Act of 1934.

This Power of Attorney shall remain in full force and effect until the undersigned is no longer required to file Forms 3, 4 and 5 with respect to the undersigned’s holdings of and transactions in securities relating to the Company, unless earlier revoked by the undersigned in a signed writing delivered to the foregoing attorneys-in-fact.

IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be executed as of this 1^st day of July, 2010.

/s/ Hobart A Smith

SMITH HOBART A 4