DATA DOMAIN, INC.

Exhibit 10.37

DATA DOMAIN, INC.

June 6, 2007

Frank Slootman

2300 Central Expressway

Santa Clara, CA 95050

Dear Frank:

We are pleased to inform you that on March 26, 2007, the Board of Directors of Data Domain, Inc. (the “Company”) approved the following provisions for accelerated vesting. The following terms apply to all Awards (as such term is defined in the Data Domain, Inc. 2007 Equity Incentive Plan (the “Plan”)) made to you and outstanding at this time, as well as any Awards to be granted to you by the Company in the future, whether or not granted under the Plan.

1.     Accelerated Vesting.  The Company hereby agrees that, if the Company is subject to a Change in Control (as such term is defined in the Plan) before your employment terminates and if you are subject to an Involuntary Termination within 12 months following the Change in Control, then you will vest in, and each option shall become exercisable for, 100% of any then unexercisable option shares and you will become vested in 100% of the unvested portion of each other Award, as of the date of the Involuntary Termination.

In addition, after the effectiveness of the IPO, Section 10.3 of the Plan shall be applicable. However, there shall be substituted for Section 10.3(d), the following: The acceleration of the exercisability of 100% of the then unexercisable portion of such Options and SARs and acceleration of vesting of 100% of the then unvested portion of the Common Shares subject to such Options and SARs, followed by the cancellation of such outstanding Options and SARs. The acceleration of exercisability of such Options and SARs and vesting of such Common Shares may be contingent on the closing of such merger or consolidation.

2.     Definitions.  For all purposes hereunder, the following terms shall be defined as specified below:

A.     “Cause” shall mean (i) your unauthorized use or disclosure of the Company’s confidential information or trade secrets, which use or disclosure causes material harm to the Company, (ii) your material failure to comply with the Company’s written policies or rules, (iii) your conviction of, or plea of “guilty” or “no contest” to, a felony under the laws of the United States or any State thereof, (iv) your gross misconduct; (v) a continuing failure to perform your assigned duties after receiving written notification of such failure from the Board, or (vi) your failure to cooperate in good faith with a governmental or internal investigation of the Company or its directors, officers or employees, if the Company has requested your cooperation.

Frank Slootman

June 6, 2007

Page 2

B.     “Involuntary Termination” shall mean either (i) your involuntary discharge by the Company for reasons other than for Cause or (ii) your voluntary resignation following (a) a change in position that involves a material reduction in your level of responsibility and/or scope of authority, (b) a reduction in your base salary (other than a reduction generally applicable to other employees similarly-situated and in general the same proportion as for you), or (c) receipt of notice that your principal workplace will be relocated more than 40 miles; for the purpose of clause (a) upon or after a Change in Control, a change in responsibility shall not be deemed to occur solely because you are part of a larger organization or because of a change in title (except for a change in the title of the Chief Executive Officer or the Chief Financial Officer).

C.    Capitalized terms not defined herein shall have the meaning ascribed to such terms in the Plan.

3.     Entire Agreement; Employment Relationship. Except as set forth above, this letter Agreement supersedes all prior agreements (whether verbal or written) between you and the Company relating to the subject matter of acceleration of vesting of option shares or other Awards on an acquisition or other Change in Control of the Company. Nothing in this letter Agreement shall affect any arrangements you currently have regarding severance or vesting benefits on termination in the absence of any acquisition or change in control. Each of the agreements evidencing options or other Awards previously granted to you shall remain in full force and effect except to the extent necessary to give effect to the terms of this letter Agreement. Nothing in this letter Agreement shall confer upon you any right to continue in employment or service for any period of specific duration. Your employment relationship is and continues to be at will.

4.     Miscellaneous.  This letter Agreement shall be binding upon the Company, its successors and assigns (including, without limitation, the surviving entity or successor party resulting from the Change in Control) and shall be construed and interpreted under the laws of the State of California.

Frank Slootman

June 6, 2007

Page 3

Please indicate your acceptance of the foregoing by signing the enclosed copy of this letter Agreement and returning it to the Company.