FIRST SUPPLEMENTAL INDENTURE

Exhibit 4.16

FIRST SUPPLEMENTAL INDENTURE

FIRST SUPPLEMENTAL INDENTURE (“First Supplemental Indenture”), dated as of September 27, 2010, among Brigham Exploration Company, a Delaware corporation (the “Company”), the Guarantors identified on the signature pages hereto (the “Guarantors”) and Wells Fargo Bank, N.A., as trustee (the “Trustee”).

WITNESSETH:

WHEREAS, the Company, the Guarantors and the Trustee have entered into an Indenture, dated as of April 20, 2006 (the “Original Indenture”), governing the Company’s 9⁵/₈% Senior Notes due 2014 (the “Notes”);

WHEREAS, under Section 9.02 of the Original Indenture, the Company, the Guarantors and the Trustee may amend the Original Indenture with the consent of the Holders of at least a majority in principal amount of the then outstanding Notes pursuant to the terms set forth therein;

WHEREAS, Holders of a majority in principal amount of outstanding Notes have consented to the amendments set forth herein in connection with the tender offer and consent solicitation of the Company commencing on September 13, 2010, with respect to the Notes (the “Tender Offer”);

WHEREAS, the Company and the Guarantors desire to enter into this First Supplemental Indenture on the date set forth above for the purpose of making the amendments set forth herein, which amendments will become operative as set forth in Section 4 herein, the execution and delivery of this First Supplemental Indenture has been authorized by the Board of Directors of the Company and of each Guarantor, and the Company and the Guarantors have requested the Trustee join with them in the execution and delivery of this First Supplemental Indenture, and in accordance with Section 9.06 and Section 12.04 of the Original Indenture have delivered an Opinion of Counsel to the Trustee stating that the First Supplemental Indenture is authorized or permitted by the Original Indenture and that all conditions precedent to its execution have been complied with; and

WHEREAS, all other conditions and requirements necessary to make this First Supplemental Indenture a valid, binding and legal instrument enforceable in accordance with its terms have been performed and fulfilled by the parties hereto, and the execution and delivery thereof have been in all respects duly authorized by the parties hereto.

NOW, THEREFORE, for and in consideration of the foregoing premises, it is mutually covenanted and agreed, for the benefit of each other and the equal and proportionate benefit of all Holders of the Notes, as follows:

1. DEFINITIONS. For all purposes of the Original Indenture and this First Supplemental Indenture, except as otherwise expressly provided or unless the context otherwise requires:

(a) References. The terms “herein,” “hereof” and other words of similar import refer to the Original Indenture and this First Supplemental Indenture as a whole and not to any particular article, section or other subdivision; and

(b) Capitalized Terms. All capitalized terms used in this First Supplemental Indenture but not defined herein shall have the meanings assigned to such terms in the Original Indenture.

2. ELIMINATION AND AMENDMENT OF CERTAIN DEFINED TERMS IN ARTICLE I OF THE ORIGINAL INDENTURE. From and as of the Operational Time (as defined in Section 4(b) of this First Supplemental Indenture), any defined terms appearing in Article One of the Original Indenture or elsewhere in the Original Indenture, and all references thereto, that are used solely in the sections, subsections or provisions of the Original Indenture deleted from the Original Indenture by virtue of Section 3 of this First Supplemental Indenture shall be deleted in their entireties from Section 1.01 of the Original Indenture.

3. AMENDMENT OF CERTAIN PROVISIONS OF ARTICLES 3, 4 AND 6 AND OTHER RELATED PROVISIONS OF THE ORIGINAL INDENTURE AND THE NOTES.

(a) Amendment of Article Three of the Original Indenture. From and as of the Operational Time, Sections 3.01, 3.02, 3.03, and 3.07 of the Original Indenture shall be amended by substituting “3” for “30” each time such number appears therein.

(b) Amendment of Article Four of Original Indenture. From and as of the Operational Time, Article 4 of the Original Indenture shall be amended by deleting Sections 4.03, 4.04, 4.05, 4.06, 4.07, 4.08, 4.09, 4.10, 4.12, 4.13, 4.14, 4.15, 4.16, 4.17, 4.18, 4.19 and 4.21 in their entireties, together with any references thereto in the Original Indenture.

(c) Amendment of Article Six of the Original Indenture. From and as of the Operational Time, Article 6 of the Original Indenture shall be amended by: (i) deleting clauses (4), (5), (6), (7), (8) and (9) of Section 6.01 in their entireties, together with any references thereto in the Original Indenture; (ii) adding “and” after “;” at the end of Section 6.01(2); and (iii) deleting ”;” at the end of Section 6.01(3) and substituting “.” therefor.

(d) Amendment of Exhibits and the Notes. From and as of the Operational Time, Exhibits A1 and A2 of the Original Indenture and the Notes shall be amended by substituting “3” for “30” each time such number appears in Sections 5 and 8 thereof.

(e) Amendment of Additional Provisions of Original Indenture and Notes. From and as of the Operational Time, any and all additional provisions of the Original Indenture and Notes shall be deemed amended to reflect the intentions of the amendments provided for in this Section 3 and elsewhere herein.

4. EFFECT OF FIRST SUPPLEMENTAL INDENTURE; OPERATION OF AMENDMENTS.

(a) Effect of First Supplemental Indenture. In accordance with Article Nine of the Original Indenture, upon the execution of this First Supplemental Indenture, the Original Indenture shall be modified in accordance herewith, and this First Supplemental Indenture shall form a part of the Original Indenture for all purposes; and every Holder of the Notes heretofore authenticated and delivered under the Original Indenture shall be bound hereby. Except as modified by this First Supplemental Indenture, the Original Indenture and the Notes, and the rights of the Holders of the Notes thereunder, shall remain unchanged and in full force and effect.

(b) Operation of Amendments. The provisions of this First Supplemental Indenture shall not become operative until the date and time (such date and time, the “Operational Time”) the Company notifies (in writing) i-Deal LLC, as depositary for the Notes under the Tender Offer (the “Depositary”), that the Company has purchased Notes tendered and not withdrawn pursuant to the Tender Offer. In the event the Company notifies (in writing) the Depositary that it has withdrawn or terminated the Tender Offer prior to the Operational Time, this First Supplemental Indenture shall be terminated and be of no force or effect and the Original Indenture shall not be modified hereby. The Company shall promptly notify the Trustee in writing of any notice it gives to the Depositary.

5. MATTERS CONCERNING THE TRUSTEE. The Trustee accepts the trusts of the Original Indenture, as amended and supplemented by this First Supplemental Indenture, and agrees to perform the same, but only upon the terms and conditions set forth in the Original Indenture, as amended and supplemented by this First Supplemental Indenture, to which the parties hereto and the Holders from time to time of the Notes agree and, except as expressly set forth in the Original Indenture, as amended and supplemented by this First Supplemental Indenture, shall incur no liability or responsibility in respect thereof. Without limiting the generality of the foregoing, the recitals contained herein shall be taken as the statements of the Company and the Guarantors, and the Trustee assumes no responsibility for their correctness, and the Trustee makes no representation as to the validity or sufficiency of the Tender Offer, any consent solicitation statement or other document used in connection with the Tender Offer, this First Supplemental Indenture or any consents thereto. This First Supplemental Indenture is executed and accepted by the Trustee subject to all the terms and conditions set forth in the Original Indenture with the same force and effect as if those terms and conditions were repeated at length herein and made applicable to the Trustee with respect hereto. In entering into this First Supplemental Indenture, the Trustee shall be entitled to the benefit of every provision of the Original Indenture relating to the conduct or affecting the liability or affording protection to the Trustee, whether or not elsewhere herein so provided.

6. RATIFICATION AND CONFIRMATION OF THE ORIGINAL INDENTURE. Except as expressly amended hereby, the Original Indenture is in all respects ratified and confirmed and all the terms, provisions and conditions thereof shall be and remain in full force and effect.

7. MISCELLANEOUS.

(a) Binding Effect. All agreements of the Company in this First Supplemental Indenture shall be binding upon the Company’s successors. All agreements of the Trustee in this First Supplemental Indenture shall be binding upon its successors.

(b) Governing Law. This First Supplemental Indenture shall be deemed to be a contract made under the laws of the State of New York and for all purposes shall be governed by and construed in accordance with the laws of the State of New York.

(c) Conflict with Trust Indenture Act of 1939. If and to the extent that any provision of this First Supplemental Indenture limits, qualifies or conflicts with the duties imposed by Sections 310-317 of the Trust Indenture Act of 1939, as amended (the “Trust Indenture Act”), by operation of Section 318(c) of the Trust Indenture Act, the imposed duties shall control.

(d) Headings for Convenience of Reference. The titles and headings of the sections of this First Supplemental Indenture have been inserted for convenience of reference only, are not to be considered a part hereof and shall in no way modify or restrict any of the terms or provisions hereof.

(e) Counterparts. This First Supplemental Indenture may be executed in any number of counterparts, each of which so executed shall be deemed to be an original, but such counterparts shall constitute but one and the same agreement.

(f) Severability. In case any provision of this First Supplemental Indenture shall be determined to be invalid, illegal or unenforceable, the validity, legality and enforceability of the remaining provisions hereof or of the Original Indenture shall not in any way be affected or impaired thereby.

(g) Effect Upon Original Indenture. This First Supplemental Indenture shall form a part of Original Indenture for all purposes, and every Holder of Notes heretofore or hereafter authenticated and delivered shall be bound hereby.

(signature page follows)

IN WITNESS WHEREOF, the Company, the Guarantors and the Trustee have caused this First Supplemental Indenture to be duly executed by their respective officers thereunto duly authorized and their respective corporate seals, duly attested, to be hereunto affixed all as of the day and the year first above written.

		BRIGHAM EXPLORATION COMPANY, a Delaware Corporation
		By:		/s/ Ben M. Brigham   Name: Ben M. Brigham
				Title: President, Chief Executive Officer and
				Chairman of the Board
		BRIGHAM, INC. a Nevada Corporation
		By:		/s/ Ben M. Brigham   Name: Ben M. Brigham
				Title: President
		BRIGHAM OIL & GAS, L.P., a Delaware limited partnership
		By: BRIGHAM, INC., its managing general partner
		By:		/s/ Ben M. Brigham   Name: Ben M. Brigham
				Title: President
		WELLS FARGO BANK, N.A., as Trustee
		By:		/s/ Jayne Sillman   Name: Jayne Sillman
				Title: Vice President