Exhibit 3.1

AMENDED AND RESTATED

CERTIFICATE OF INCORPORATION

OF

BRIGHAM EXPLORATION COMPANY

FIRST: The name of the corporation is Brigham Exploration Company (the “Corporation”).

SECOND: The address of its registered office in the State of Delaware is 1209 Orange Street, in the City of Wilmington, County of New Castle 19801. The name of its registered agent at such address is The Corporation Trust Company.

THIRD: The nature of the business or purposes to be conducted or promoted is to engage in any lawful act or activity for which corporations may be organized under the General Corporation Law of the State of Delaware (the “DGCL”).

FOURTH: The total number of shares of all classes of stock which the Corporation shall have authority to issue is 1,000 shares of common stock, par value $0.01 per share (the “Common Stock”). Each share of Common Stock is entitled to one vote.

FIFTH: Unless and except to the extent that the bylaws of the Corporation shall so require, the election of directors of the Corporation need not be by written ballot.

SIXTH: In furtherance of, and not in limitation of, the powers conferred by statute, the bylaws of the Corporation may be altered, amended or repealed and new bylaws may be adopted by the Board of Directors of the Corporation (the “Board”), unless the bylaws of the Corporation limit or eliminate the Board’s power to amend, alter or repeal the bylaws or to adopt new bylaws.

SEVENTH: Whenever a compromise or arrangement is proposed between the Corporation and its creditors or any class of them and/or between the Corporation and its stockholders or any class of them, any court of equitable jurisdiction within the State of Delaware may, on the application in a summary way of the Corporation or of any creditor or stockholder thereof or on the application of any receiver or receivers appointed for the Corporation under Section 291 of the DGCL or on the application of trustees in dissolution or of any receiver or receivers appointed for the Corporation under Section 279 of the DGCL, order a meeting of the creditors or class of creditors, and/or of the stockholders or class of stockholders of the Corporation, as the case may be, to be summoned in such manner as the said court directs. If a majority in number representing three fourths in value of the creditors or class of creditors, and/or of the stockholders or class of stockholders of the Corporation, as the case may be, agree to any compromise or arrangement and to any reorganization of the Corporation as a consequence of such compromise or arrangement, the said compromise or arrangement and the said reorganization shall, if sanctioned by the court to which the said application has been made, be binding on all the creditors or class of creditors, and/or on all the stockholders or class of stockholders, of the Corporation, as the case may be, and also on the Corporation.

EIGHTH: Elimination of Certain Liability of Directors. (a) To the fullest extent permitted by the DGCL as the same exists or may hereafter be amended, a director of the

Corporation shall not be personally liable to the Corporation or its stockholders for monetary damages for breach of duty as a director. Without limiting the foregoing in any respect, a director of the Corporation shall not be personally liable to the Corporation or its stockholders for monetary damages for breach of duty as a director, except for liability (i) for any breach of the director’s duty of loyalty to the Corporation or its stockholders, (ii) for acts or omissions not in good faith or which involve intentional misconduct or a knowing violation of law, (iii) under Section 174 of the DGCL, or (iv) for any transaction from which the director derived an improper personal benefit. If the DGCL is amended to authorize corporate action further eliminating or limiting the personal liability of directors, then the liability of a director of the Corporation shall be eliminated or limited to the fullest extent permitted by the DGCL, as so amended. Any repeal or modification of this provision shall not adversely affect any right or protection of a director of the Corporation existing at the time of such repeal or modification.

(i) Right to Indemnification. (A) Each person who was or is made a party or is threatened to be made a party to or is involved in any action, suit or proceeding, whether civil, criminal, administrative or investigative (hereinafter a “proceeding”), by reason of the fact that he or she, or a person of whom he or she is the legal representative, is or was a director or officer of the Corporation, or serves, in any capacity, any corporation, partnership or other entity in which the Corporation has a partnership or other interest, including service with respect to employee benefit plans, whether the basis of such proceeding is alleged action in an official capacity as a director, officer, employee or agent or in any other capacity while serving as a director, officer, employee or agent, shall be indemnified and held harmless by the Corporation to the fullest extent authorized by the DGCL, as the same exists or may hereafter be amended (but, in case of any such amendment, only to the extent that such amendment permits the Corporation to provide broader indemnification rights than said law permitted the Corporation to provide prior to such amendment), against all expense, liability and loss (including attorneys’ fees, judgments, fines, ERISA excise taxes or penalties and amounts paid or to be paid in settlement) reasonably incurred or suffered by such person in connection therewith and such indemnification shall continue as to a person who has ceased to be a director, officer, employee or agent and shall inure to the benefit of his or her heirs, executors and administrators, and (B) the Corporation shall indemnify and hold harmless in such manner any person designated by the Board, or any committee thereof, as a person subject to this indemnification provision, and who was or is made a party or is threatened to be made a party to a proceeding by reason of the fact that he, she or a person of whom he or she is the legal representative, is or was serving at the request of the Board of the Corporation as a director, officer, employee or agent of another corporation or a partnership, joint venture, trust or other enterprise whether such request is made before or after the acts taken or allegedly taken or events occurring or allegedly occurring which give rise to such proceeding; provided, however, that except as provided in subsection (b)(ii) of this Section, the Corporation shall indemnify any such person seeking indemnification pursuant to this subsection in connection with a proceeding (or part thereof) initiated by such person only if such proceeding (or part thereof) was authorized by the Board. The right to indemnification conferred herein shall be a contract right based upon an offer from the Corporation which shall be deemed to have been made to a

person subject to subsection (b)(i)(A) on the date hereof and to a person subject to subsection (b)(i)(B) on the date designated by the Board, shall be deemed to be accepted by such person’s service or continued service as a director or officer of the Corporation for any period after the offer is made and shall include the right to be paid by the Corporation the expenses incurred in defending any such proceeding in advance of its final disposition; provided, however, that if the DGCL requires, the payment of such expenses incurred by a director or officer in his or her capacity as the director or officer (and not in any other capacity in which service was or is rendered by such person while a director or officer, including, without limitation, service to an employee benefit plan) in advance of the final disposition of a proceeding, shall be made only upon delivery to the Corporation of an undertaking, by or on behalf of such director or officer, to repay all amounts so advanced if it shall ultimately be determined that such director or officer is not entitled to be indemnified under this Section or otherwise. The Corporation may, by action of the Board, provide indemnification to employees or agents of the Corporation with the same scope and effect as the foregoing indemnification of directors and officers.

(ii) Right of Claimant to Bring Suit. If a claim under Section (b)(i) of this Article is not paid in full by the Corporation within thirty days after a written claim has been received by the Corporation, the claimant may at any time thereafter bring suit against the Corporation to recover the unpaid amount of the claim and, if successful in whole or in part, the claimant shall be entitled to be paid also the expense of prosecuting such claim. It shall be a defense to any such action (other than an action brought to enforce a claim for expenses incurred in defending any proceeding in advance of its final disposition where the required undertaking, if any is required, has been tendered to the Corporation) that the claimant has not met the standards of conduct which make it permissible under the DGCL for the Corporation to indemnify the claimant for the amount claimed. Neither the failure of the Corporation (including the Board, independent legal counsel, or its stockholders) to have made a determination prior to the commencement of such action that indemnification of the claimant is proper in the circumstances because he or she has met the applicable standard of conduct set forth in the DGCL, nor an actual determination by the Corporation (including the Board, independent legal counsel, or its stockholders) that the claimant has not met such applicable standard of conduct, shall be a defense to the action or create a presumption that the claimant has not met the applicable standard of conduct.

(iii) Nonexclusivity of Rights. The right to indemnification and the payment of expenses incurred in defending a proceeding in advance of its final disposition conferred in this Section shall not be exclusive of any right which any person may have or hereafter acquire under any statute, provision of the Certificate of Incorporation, by-law, agreement, vote of stockholders or disinterested directors or otherwise.

(iv) Insurance. The Corporation may maintain insurance, at its expense, to protect itself and any director officer, employee or agent of the Corporation or another corporation, partnership, joint venture, trust or other enterprise against any such expense, liability or loss, whether or not the corporation would have the power to indemnify such person against such expense, liability or loss under the DGCL.

(v) Nature of Rights. The rights conferred upon indemnitees in this Article EIGHTH shall be contract rights and such rights shall continue as to an indemnitee who has ceased to be a director, officer, employee or agent and shall inure to the benefit of the indemnitee’s heirs, executors and administrators. Any amendment, alteration or repeal of this Article EIGHTH that adversely affects any right of an indemnitee or its successors shall be prospective only and shall not limit, eliminate, or impair any such right with respect to any proceeding involving any occurrence or alleged occurrence of any action or omission to act that took place prior to such amendment or repeal.

(vi) Severability. If any subsection of this Section (b) shall be deemed to be invalid or ineffective in any proceedings, the remaining subsections hereof shall not be affected and shall remain in full force and effect.

NINTH: The Corporation shall have the right, subject to any express provisions or restrictions contained in this Certificate of Incorporation or bylaws of the Corporation, from time to time, to amend this Certificate of Incorporation or any provision hereof in any manner now or hereafter provided by law, and all rights and powers of any kind conferred upon a director or stockholder of the Corporation by this Certificate of Incorporation or any amendment hereof are subject to such right of the Corporation.