Filed by Bowne Pure Compliance







Exhibit 10.42




AGREEMENT RELATING TO VOTING OF SHARES




This AGREEMENT RELATING TO VOTING OF SHARES (this “Agreement”), is entered into July 31, 2008 by and between DLJ
Merchant Banking Partners III, L.P., DLJ Offshore Partners III, C.V., DLJ Offshore Partners III-1, C.V., DLJ Offshore
Partners III-2, C.V., DLJ MB PartnersIII GmbH & Co. KG, Millennium Partners II, L.P., MBP III Plan Investors, L.P., DLJ
ESC II, L.P. and DLJMB Funding III, Inc. (collectively, the “CS Entities”), and Brigham Exploration Company, a Delaware
corporation (the “Company”).



WHEREAS, the CS Entities own more than 9.99% of the common stock of the Company (the “Common Stock”);



WHEREAS, the CS Entities have determined that it is no longer necessary to retain their right to nominate a
representative to the Board of Directors of the Company and are entering into an Amendment to Securities Purchase
Agreement to relinquish that right;



WHEREAS, the CS Entities have also determined to limit the number of shares of Common Stock that they will vote at
any stockholders’ meeting of the Company;



NOW, THEREFORE, for good and valuable consideration the receipt and sufficiency of which are hereby acknowledged
and confessed, and in consideration of the premises and the mutual covenants and agreements herein contained, and
intending to be legally bound hereby, the Company and the CS Entities hereby agree as follows:



1. Agreement to Limit Voting of Shares. Regardless of the number of shares of Common Stock owned by them
at any time, the CS Entities will not vote more than 9.99% of the outstanding shares of Common Stock whether at a
meeting of the stockholders of the Company or otherwise. Without limiting the foregoing, all of the shares of Common
Stock owned by the CS Entities will retain their character as outstanding shares of Common Stock entitled to vote on
any matter submitted to the stockholders of the Company. For purposes of this Section 1, shares of Common Stock that
are present at a meeting and that abstain on any matter will not be considered to have been voted on that matter.



2. No Company Liability. The CS Entities undertake to ensure that the requirements of Section 1 are
fulfilled. The Company will not be liable to the CS Entities or to any other person for any claims arising from the
Company’s good faith efforts to enforce the requirements of Section 1 or for any claims arising from the Company’s
failure to enforce the requirements of Section 1.



3. Indemnification. The CS Entities, severally and not jointly, shall indemnify and hold the Company and
each of its directors, officers, employees and agents (each a “Company Party”), harmless from any and all
losses, liabilities, obligations, claims, contingencies, damages, costs, and expenses (including all court costs and
reasonable attorneys’ fees) that any Company Party may suffer or incur as a result of, arising out of or in connection
with this Agreement or anything done or omitted to be done by such Company Party in connection with this Agreement,
including the negligence or alleged negligence of any Company Party, but excluding the gross negligence, fraud
or willful misconduct of any Company Party.


 


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4. Amendment; Waiver. This Agreement may not be amended except by an instrument in writing signed by or
on behalf of all the parties hereto. No failure or delay by a party hereto in exercising any right, power, or
privilege hereunder shall operate as a waiver thereof nor shall any single or partial exercise thereof preclude any
other or further exercise thereof or the exercise of any other right, power, or privilege. The provisions of this
Agreement may not be waived except by an instrument in writing signed by or on behalf of the party against whom such
waiver is sought to be enforced.



5. No Third Party Beneficiaries. Nothing in this Agreement, express or implied, is intended to or shall
confer upon any person other than the parties hereto, and their respective successors and permitted assigns, any
rights, benefits or remedies of any nature whatsoever under or by reason of this Agreement.



6. Counterparts. This Agreement may be executed by the parties hereto in any number of counterparts, each
of which shall be deemed an original but all of which shall constitute one and the same Agreement. Each counterpart
may consist of a number of copies hereof, each signed by less than all, but together signed by all of the parties
hereto.



IN WITNESS WHEREOF, the parties have executed this Agreement or caused this Agreement to be executed by their duly
authorized representatives, all as of the day and year first above written.



THE COMPANY:



BRIGHAM EXPLORATION COMPANY



By: /s/ Eugene B. Shepherd, Jr.                 

Name: Eugene B. Shepherd, Jr.

Title: Chief Financial Officer




CS ENTITIES



DLJ MERCHANT BANKING PARTNERS III, L.P.



By: DLJ Merchant Banking III, Inc.,



       Its Managing General Partner



By: /s/ William Spiro                               

Name: William Spiro

Title: Vice President




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DLJ MERCHANT BANKING III, INC., as Advisory General Partner on behalf of DLJ OFFSHORE PARTNERS III, C.V.



By: /s/ William Spiro                                     

Name: William Spiro

Title: Vice President




DLJ MERCHANT BANKING III, INC., as Advisory General Partner on behalf of DLJ OFFSHORE PARTNERS III-1, C.V. and as
attorney-in-fact for DLJMB III (Bermuda), L.P., as Associate General Partner of DLJ OFFSHORE PARTNERS III-1, C.V.



By: /s/ William Spiro                                    

Name: William Spiro

Title: Vice President




DLJ MERCHANT BANKING III, INC., as
Advisory General Partner on behalf of DLJ OFFSHORE PARTNERS III-2, C.V. and as attorney-in-fact for DLJMB III
(Bermuda), L.P., as Associate General Partner of DLJ OFFSHORE PARTNERS III-2, C.V.



By: /s/ William Spiro                                  

Name: William Spiro

Title: Vice President




DLJ MERCHANT BANKING III, INC., as General Partner of DLJ Merchant Banking III, L.P. and as attorney-in-fact for DLJ
Merchant Banking III, L.P. as Managing Limited Partner for and on behalf of DLJ MB PARTNERSIII GmbH & Co. KG



By: /s/ William Spiro                                    

Name: William Spiro

Title: Vice President




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DLJ MB GmbH, as General Partner for and on behalf of DLJ MB PARTNERSIII GmbH & Co. KG



By: /s/ Edward Nadel                                   

Name: Edward Nadel

Title: Director




MILLENNIUM PARTNERS II,, INC.L.P.



By: DLJ Merchant Banking III, Inc.,



       Its Managing General Partner



By: /s/ William Spiro                                  

Name: William Spiro

Title: Vice President




MBP III PLAN INVESTORS, L.P.



By: DLJ LBO Plans Management Corporation II,



       Its General Partner



By: /s/ William Spiro                                 

Name: William Spiro

Title: Vice President




DLJ ESC II, INC.L.P.



By: DLJ LBO Plans Management Corporation,



       Its General Partner



By: /s/ William Spiro                                

Name: William Spiro

Title: Vice President




DLJMB FUNDING III, INC.



By: /s/ William Spiro                                

Name: William Spiro

Title: Vice President




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