Exhibit 99.3

Brencourt Advisors, LLC

600 Lexington Avenue, 8th Floor

New York, NY 10022

June 20, 2007

Thomas W. Smith

Scott J. Vassalluzzo

323 Railroad Avenue

Greenwich, CT 06830

Gentlemen:

This Letter Agreement confirms the (i) agreement by Brencourt Advisors, LLC (“Brencourt”) to purchase for the account and on behalf of one or more funds managed by Brencourt (collectively, the “Purchasers”) an aggregate of 1,807,021 shares (the “Shares”) of common stock, par value $.01 per share (the “Common Stock”) of Vertrue Incorporated, a Delaware corporation (the “Company”) (CUSIP # 92534N101) from you and certain accounts managed by you (collectively, the “Sellers”) for a fixed price of $48.90 per Share (subject to adjustment as provided below), resulting in an aggregate purchase price of $88,363,326.90, and (ii) the agreement by you to sell for the account and on behalf of Sellers the Shares to the Purchasers for such price, in each case subject to the terms and conditions hereof. Such purchase price per Share shall be adjusted so that, for each day that the Closing occurs prior to July 10, 2007, the price per Share shall be reduced by $0.007, and for each day that the Closing occurs after July 10, 2007, the price per Share shall be increased by $0.007 (for example, a closing on July 6, 2007 would result in a purchase price per Share of $48.872; and a closing on July 11, 2007 would result in a purchase price per Share of $48.907.

1. Closing. The closing of such purchase and sale (the “Closing”) shall occur on the second business day after receipt by Brencourt and/or the Purchasers of notice of the termination of the applicable waiting period under the Hart-Scott-Rodino Antitrust Improvements Act of 1976 (the “HSR Act”), or the expiration of the waiting period thereunder. The aggregate purchase price for the Shares shall be paid by wire transfer by the Purchasers on the date of the closing to such accounts as you shall have specified in writing.

2. Representations and Warranties.

(a) Brencourt represents and warrants to you, and you represent and warrant to Brencourt, that such party is duly authorized to execute, deliver and perform its obligations hereunder and that such execution, delivery and performance do not and will not conflict with or constitute a breach of any law, regulation or contract binding on such party. Brencourt represents and warrants that it has all necessary power and authority to act on behalf of and to bind the Purchasers to purchase the Shares and fulfill all the obligations of Purchasers contemplated by this Agreement, and that the Purchasers presently have and will have at the time of Closing sufficient funds to pay the full cash aggregate purchase price. You represent and warrant that you have all necessary power and authority to act on behalf of and to bind the Sellers to sell the Shares and fulfill all the obligations of Sellers contemplated by this Agreement.

(b) You represent that the Sellers own all of the Shares free and clear of any lien, claim or other encumbrance, except for any that will be released or satisfied upon the sale to the Purchasers hereunder.

3. Voting Agreement.

(a) Agreement to Vote. Subject to Section 7 of this Agreement, effective on the date hereof, you agree that at any meeting of the stockholders of the Company (a “Company Stockholders’ Meeting”), for which a Seller is a record holder of any of the Shares and at every adjournment or postponement thereof, or in any other circumstances upon which a vote, consent, or other approval (including by written consent) is sought, the Sellers shall—

(i) when a meeting is held, appear at such meeting or otherwise cause the Shares to be counted as present thereat for purposes of establishing a quorum,

(ii) vote, or execute consents in respect of the Shares, or cause the Shares to be voted, or consents to be executed in respect thereof, in respect of the Agreement and Plan of Merger (the “Merger Agreement”) between the Company and Velo Holdings Inc. and Velo Acquisition Inc. (including any revised or amended Merger Agreement approved by the board of directors of the Company), as Brencourt may direct in writing, and

(iii) vote, or execute consents in respect of the Shares to be voted, or consents to be executed in respect thereof, as Brencourt may direct in writing, in respect of (A) any agreement or transaction relating to an Acquisition Proposal (as defined in the Merger Agreement) or transaction or occurrence that if proposed and offered to the Company or its stockholders (or any of them) would constitute an Acquisition Proposal or (B) any extraordinary corporate transaction (other than the Merger), or any amendment of the Company’s Certificate of Incorporation or Bylaws or other proposal, action or transaction involving the Company or any of the Company Subsidiaries or any of its stockholders, and

(iv) vote, or execute consents in respect of the Shares to be voted, or consents to be executed in respect thereof, as Brencourt may direct in writing, in respect of any other matter that may be presented to the stockholders of the Company for which the Sellers are the record holders of the Shares.

(b) Appointment of Proxy. Subject to Section 7 of this Agreement, you hereby irrevocably (to the fullest extent permitted by law) constitute and appoint Marc Nuccittelli and William Collins, each of them individually, as the Sellers’ proxy and attorney-in-fact, with full power of substitution and resubstitution, to cause the Shares to be counted as present at any such Company Stockholders’ Meetings and to vote the Shares at any Company Stockholders’ Meeting, however called, and to execute consents in respect of the Shares as and to the extent provided in Section (a) hereof.

(c) Revocation of Other Proxies. You represent that any proxies heretofore given in respect of the Shares, if any, are revocable, and hereby revoke all other proxies and powers of attorney with respect to the Shares that the Sellers may have heretofore appointed or granted, and no subsequent proxy or power of attorney shall be granted.

(d) Proxy Irrevocable. You acknowledge that Purchasers are relying on this Agreement in purchasing the Shares. ACCORDINGLY, SUBJECT TO SECTION 7 OF THIS AGREEMENT, THIS PROXY AND POWER OF ATTORNEY IS IRREVOCABLE(TO THE FULLEST EXTENT PERMITTED BY LAW) AND COUPLED WITH AN INTEREST. Except as otherwise required by law in the case of Shares beneficially owned by Sellers who are natural persons (other than yourselves), this irrevocable proxy shall not be terminated by any act of the Sellers (subject to Section 7 of this Agreement) or by operation of law, whether by the death or incapacity of the Sellers or by the occurrence of any other event or events (including, without limiting the foregoing, the termination of any trust or estate for which either of you is acting as a fiduciary or fiduciaries or the dissolution or liquidation of any corporation or partnership). If after the execution hereof any Seller should be dissolved or liquidated, actions taken by the Purchasers hereunder shall be as valid as if such dissolution, liquidation or other event or events had not occurred, regardless of whether or not the Purchasers have received any notice of such dissolution, liquidation or other event.

(e) No Transfer of Rights. Except as otherwise provided in Section 5 of this Agreement with respect to the Merger, the Sellers shall not: (i) enter into any tender, voting, or other such agreement, or grant any proxy, power-of-attorney or other authorization or consent with respect to any of the Shares; or (ii) take any other action that would in any way restrict, limit or interfere with the performance of its obligations hereunder or the transactions contemplated hereby or make any representation or warranty of the Sellers untrue or incorrect. Except as contemplated by this Agreement, the Sellers will not enter into any voting or other agreement or grant any power of attorney with respect to the Shares, or take any action that is inconsistent with this Agreement.

4. HSR Filing. Brencourt and Purchasers shall use their best efforts to prepare and file a Notification and Report Form with the United States Federal Trade Commission and the Antitrust Division of the United States Department of Justice no later than two business days after the date of this Agreement, and to take all further actions as may be required to obtain the early termination of the waiting period under the HSR Act or the earliest possible expiration of the waiting period thereunder. Brencourt and Purchasers shall be solely responsible for all applicable costs and expenses, including the filing fee.

5. Additional Purchasers’ Obligations. If, for any reason other than as a result of a material breach by you under this Agreement, the Closing of the purchase and sale of the Shares under this Agreement does not occur prior to the closing of the Merger (as defined in the Merger Agreement and any amendments to the Merger Agreement), the Purchasers shall be obligated to pay you the amount of $0.25 per Share, or an aggregate payment of $451,755.25, which payment shall be made by wire transfer by the Purchasers to such accounts as you shall have specified in writing and shall be paid no later than two business days after the closing of the Merger. In such case where the Closing of the purchase and sale of the Shares under this Agreement does not occur prior to the closing of the Merger, Sellers shall retain all rights that they have with respect to their Shares under the Merger Agreement, and the parties shall have no further obligations under this Agreement other than Purchasers’ obligation to make the payment of $451,755.25.

6. Miscellaneous. Brencourt’s and Purchasers’ obligations under this Agreement shall not be excused if, for any reason, you are unable to perform your obligations with respect to all of the Shares, provided that you perform your obligations with respect to a minimum of 1,500,000 Shares. In any such case, neither you nor any Seller shall have any liability under this Agreement, and the parties shall enter into an appropriate amendment to this Agreement so that

the provisions of this Agreement only shall apply to the Shares for which and the Sellers for whom you are able to perform the obligations under this Agreement.

7. Termination. You may terminate this Agreement if the Closing shall not have occurred on or prior to July 31, 2007, other than as a result of a breach by you of your obligations under this Agreement. In the event of a termination of this Agreement, the voting agreement and proxy provided in Section 3 of this Agreement shall likewise terminate.

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If the foregoing accurately states our agreement, please sign and return a copy hereof, at which time this will become a mutually binding agreement.

Very truly yours,

BRENCOURT ADVISORS, LLC

By: /s/ Michael Palmer

Name: Michael Palmer

Title: Chief Financial Officer

/s/Thomas W. Smith

Thomas W. Smith

/s/Scott J. Vassalluzzo

Scott J. Vassalluzzo

VERTRUE INC SC 13D/A