AMENDMENT TO THE CHANGE OF CONTROL AGREEMENT

Exhibit 10.50

AMENDMENT TO THE

This Amendment to the Change of Control Agreement (the “Amendment”) is made and entered into effective as of January 1, 2009, by and between Brigham Exploration Company, a Delaware corporation (the “Company”) and                      , an officer of the Company (“Officer”).

W I T N E S S E T H :

WHEREAS, the Company and Officer entered into a Change of Control Agreement effective as of                      (the “Agreement”); and

WHEREAS, the Company and Officer now desire to amend the Agreement for compliance with Internal Revenue Code Section 409A and the Treasury Regulations thereunder;

NOW, THEREFORE, in consideration of the premises, the parties do hereby agree as follows:

1. Paragraph 1(a) of the Agreement is hereby amended and restated in its entirety as follows:

(a) Severance Payment . Upon the occurrence of a Termination Event (as defined in Paragraph 2) during the Retention Period and Officer’s execution of the General Release within 45 days following the Termination Date (and provided that Officer does not revoke the General Release within any revocation period) —

(i) the Company or its successor shall pay Officer an amount equal to Officer’s Annual Base Salary (as defined in Paragraph 2) multiplied by 2.0, payable as a lump sum cash payment on the 60 ^th day following the Termination Date;

(ii) if Officer was participating in a life insurance and/or disability benefit plan maintained by the Company as of [his/her] Termination Date, such coverage will be continued at the same cost, if any, charged to similarly situated active employees under such plans for a period of eighteen months following the Termination Date or, if earlier, the date as of which Officer obtains other employment. Officer shall immediately notify the Company upon obtaining other employment;

(iii) if Officer was participating in a hospital, surgical, medical or dental benefit plan maintained by the Company as of [his/her] Termination Date, then Officer will be entitled to continue such participation on the same terms and at the same cost as similarly-situated current employees until the date as of which Officer obtains other employment, provided that such coverage is either nontaxable to Officer or otherwise exempt from Code Section 409A. Officer shall immediately notify the Company upon obtaining other employment; and

(iv) for a period of five years following a Change of Control, the Company shall pay all reasonable legal fees and expenses promptly as they are incurred by Officer in seeking to obtain or enforce any right or benefit provided by this Agreement other than fees or expenses incurred in connection with any challenge by Officer to the enforceability of the General Release. In no event shall the payment of eligible fees and expenses be made later than the last day of Officer’s taxable year following the taxable year in which such fees and expenses are incurred. The amount of fees and expenses eligible for payment during Officer’s taxable year shall not affect the fees and expenses eligible for payment in any other taxable year.

2. Paragraph 1(b) of the Agreement is hereby amended and restated in its entirety as follows:

(b) Option Vesting . In the event of a Change of Control, any option to purchase Brigham common stock held by Officer shall immediately vest with respect to any portion of such option which has not then vested but is scheduled to vest within five years of the date of the Change of Control.

3. The second Paragraph 2(f) of the Agreement is hereby amended to be Paragraph 2(g) and the current Paragraph 2(g) of the Agreement is hereby amended to be Paragraph 2(h).

4. Paragraph 2(h)(ii) of the Agreement is hereby amended and restated in its entirety as follows:

(ii) Officer shall voluntarily terminate [his/her] employment with the Company or any successor thereto (or an affiliate of the Company or any successor thereto) for “Good Reason.” To ex