FIRST AMENDMENT

Exhibit 10.33

FIRST AMENDMENT

This FIRST AMENDMENT (“Amendment”) dated as of May 16, 2011 (the “Effective Date”) is by and among Brigham Oil & Gas, L.P., a Delaware limited partnership (the “Borrower”), Brigham Exploration Company, a Delaware corporation (“Brigham Exploration”), Brigham Inc., a Nevada corporation (the “General Partner”, together with Brigham Exploration, each a “Guarantor” and collectively the “Guarantors”, and together with Brigham Exploration and the Borrower, each a “Credit Party” and collectively the “Credit Parties”), the Lenders party hereto, and Bank of America, N.A., as administrative agent for the Lenders (in such capacity, the “Administrative Agent”).

WHEREAS, the Borrower, the Guarantors, the lenders from time to time party thereto (the “Lenders”), and the Administrative Agent are parties to the Fifth Amended and Restated Credit Agreement, dated as of February 23, 2011 (the “Credit Agreement”);

WHEREAS, the parties hereto have agreed to make certain amendments to the Credit Agreement as provided for herein, subject to the conditions herein;

NOW THEREFORE, in consideration of the premises and the mutual covenants, representations and warranties contained herein, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto hereby agree as follows:

AGREEMENT

Section 1. Defined Terms. Unless otherwise defined in this Amendment, each capitalized term used in this Amendment has the meaning given such term in the Credit Agreement.

Section 2. Amendment to the Credit Agreement.

(a) Section 1.01 of the Credit Agreement is hereby amended by inserting the following new definitions in their appropriate alphabetical order:

“2011 Permitted Senior Notes” means the Permitted Senior Notes issued and sold during the period from the First Amendment Effective Date through the date of the Borrowing Base redetermination provided for in Section 2.02(b) scheduled to occur after the delivery of the Internal Engineering Report due October 1, 2011.

“First Amendment Effective Date” means May 16, 2011.

(b) Section 1.01 of the Credit Agreement is hereby amended by replacing the definition of “Maximum Permitted Senior Note Amount” with the following definition:

“Maximum Permitted Senior Note Amount” means $300,000,000; provided that in connection with the issuance of the 2011 Permitted Senior Notes the Maximum Permitted Senior Note Amount shall automatically increase (up to but not exceeding $600,000,000) by an amount equal to (i) the stated aggregate principal amount of the 2011 Permitted Senior Notes issued minus (ii) the aggregate principal amount of any Permitted Senior Notes redeemed, retired or purchased with the proceeds from the sale or issuance of the 2011 Permitted Senior Notes.

Section 3. Conditions to Effectiveness. This Amendment shall become effective as of the Effective Date when the Administrative Agent has received counterparts hereof duly executed by the Borrower, each Guarantor, the Administrative Agent and the Majority Lenders.

Section 4. Representations and Warranties. Each Credit Party hereby represents and warrants that after giving effect hereto:

(a) the representations and warranties of such Credit Party contained in the Loan Documents are true and correct in all material respects on and as of the Effective Date, other than those representations and warranties that expressly relate solely to a specific earlier date, which shall remain correct as of such earlier date; and

(b) no Default or Event of Default has occurred and is continuing.

Section 5. Reaffirmation of Guaranty. Each Guarantor hereby ratifies, confirms, and acknowledges that its obligations under the Credit Agreement are in full force and effect and that each Guarantor continues to unconditionally and irrevocably, jointly and severally, guarantee the full and punctual payment, when due, whether at stated maturity or earlier by acceleration or otherwise, all of the Obligations (subject to the terms of Article VIII of the Credit Agreement), as such Obligations may have been amended by this Amendment. Each Guarantor hereby acknowledges that its execution and delivery of this Amendment does not indicate or establish an approval or consent requirement by the Guarantors in connection with the execution and delivery of consents, waivers or amendments to the Credit Agreement or any of the other Loan Documents.

Section 6. Effect of Amendment,

(a) The execution, delivery and effectiveness of this Amendment shall not, except as expressly provided herein, operate as a waiver of any right, power or remedy of any Lender, the Issuing Lender or the Administrative Agent under any of the Loan Documents, nor, except as expressly provided herein, constitute a waiver or amendment of any provision of any of the Loan Documents.

(b) Upon and after the execution of this Amendment by each of the parties hereto, each reference in the Credit Agreement to “this Agreement”, “hereunder”, “hereof” or words of like import referring to the Credit Agreement, and each reference in the other Loan Documents to “the Credit Agreement”, “thereunder”, “thereof” or words of like import referring to the Credit Agreement, shall mean and be a reference to the Credit Agreement as modified hereby.

(c) This Amendment is a Loan Document executed pursuant to the Credit Agreement and shall (unless otherwise expressly indicated herein) be construed, administered and applied in accordance with the terms and provisions thereof.

(d) Except as specifically modified above, the Credit Agreement and the other Loan Documents are and shall continue to be in full force and effect and are hereby in all respects ratified and confirmed.

Section 7. Governing Law. THIS AMENDMENT SHALL BE CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK AND THE APPLICABLE LAWS OF THE UNITED STATES OF AMERICA.

Section 8. Counterparts. This Amendment may be executed in any number of counterparts and by different parties hereto in separate counterparts, each of which when so executed shall be deemed to be an original and all of which taken together shall constitute one and the same agreement. Transmission by facsimile of an executed counterpart of this Amendment, or of an executed signature page of this Agreement, shall be deemed to constitute due and sufficient delivery of such counterpart.

[Remainder of Page Intentionally Left Blank]

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed and delivered by their respective duly authorized officers to be effective as of the Effective Date.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.

Signature Page to First Amendment to Credit Agreement
Brigham Oil & Gas, L.P.