Exhibit 10.1

FOURTH AGREEMENT REGARDING PRIVATE PLACEMENT OF SECURITIES

OF

SUNESIS PHARMACEUTICALS, INC.

THIS AGREEMENT (the “Agreement”) is made and entered into as of this 29^th day of March, 2010, by and among SUNESIS PHARMACEUTICALS, INC., a Delaware corporation (the “Company”), and the persons and entities listed on Exhibit A hereto (the “Investors”).

RECITALS

A. The Company and the Investors wish to amend that certain Investor Rights Agreement, dated April 3, 2009, as amended June 29, 2009 and October 27, 2009 (as amended, the “Rights Agreement”), by and among the Company and the Investors (as defined in the Rights Agreement);

B. Pursuant to Section 8(c) of the Rights Agreement, Section 7(b) of the Rights Agreement may be amended only by written consent of the Company, the Majority Investors (as defined in the Rights Agreement) and Alta Partners, Bay City Capital, NEA and Nextech (each as defined in the Rights Agreement); and

C. The undersigned hold or have the right to acquire at least a majority-in-interest of the total Unit Shares and constitute the Majority Investors and include Alta Partners, Bay City Capital, NEA and Nextech (collectively, the “Requisite Investors”).

AGREEMENT

NOW, THEREFORE, in consideration of these premises and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

1. AMENDMENT TO RIGHTS AGREEMENT. All capitalized terms not otherwise defined in this Section 2 shall be as defined in the Rights Agreement. The Company and the undersigned hereby agree that Section 7(b)(2) of the Rights Agreement is hereby amended and restated to read as follows:

“Subject to Section 7(b)(6) below, from and after the earlier to occur of (i) the Second Unit Closing, (ii) the Common Equity Closing and (iii) the closing of an Alternative Common Stock Financing in which the Investors exercise preemptive rights pursuant to the terms of this Agreement and, as a result, beneficially own greater than a majority of the Company’s voting stock as of such closing, the Company shall take all appropriate action to promptly establish and maintain the size of the Board at nine (9) members, five (5) of which shall be Investor Designees and nominated in accordance with the provisions of this Section 7(b). Alta Partners, Bay City Capital, NEA and Nextech, together with their respective affiliates, shall each have the right to designate one (1) such Investor Designee. Notwithstanding the foregoing, the Company’s obligation to set and maintain the size of the Board at nine (9) members and the Investors’ right to designate five (5) Investor Designees pursuant to this Section 7(b)(2) shall not be effective prior to May 1, 2010 or such later date as determined by the Majority Investors. On or prior to January 20 of each year in which the Majority Investors have rights pursuant to this Section 7(b) (assuming the Company has made a request therefor at least five (5) Trading Days prior thereto), and within five (5) Trading Days of the request by the Company in connection with the preparation of a proxy statement with respect to the election of members of the Board or a vacancy created on

1.

the Board by the resignation, death or disability of an Investor Designee or the failure of an Investor Designee to be elected at a meeting of the Company at any time at which the Majority Investors have rights pursuant to this Section 7(b), each Investor shall notify the Company of the number of voting shares of the Company’s capital stock beneficially owned by such Investor as of a date within five (5) Trading Days of the delivery of such notice.”

2. MISCELLANEOUS. This Agreement may be executed in two or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument. A facsimile, telecopy or other reproduction of this Agreement may be executed by one or more parties hereto and delivered by such party by facsimile or any similar electronic transmission device pursuant to which the signature of or on behalf of such party can be seen. Such execution and delivery shall be considered valid, binding and effective for all purposes. At the request of any party hereto, all parties hereto agree to execute and deliver an original of this Agreement as well as any facsimile, telecopy or other reproduction hereof. Other than as set forth herein, the Rights Agreement shall remain in full force and effect. All questions concerning the construction, validity, enforcement and interpretation of this Agreement shall be governed by and construed and enforced in accordance with the internal laws of the State of California, without regard to the principles of conflicts of law thereof. Upon the execution of this Agreement by the Company and the Requisite Investors, all parties to the Rights Agreement shall be bound by this Agreement.

[SIGNATURE PAGE TO FOLLOW]

2.

IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the date first above written.

EXHIBIT A

LIST OF INVESTORS

Bay City Capital Fund V, L.P.

Bay City Capital Fund V Co-Investment Fund, L.P.

Growth Equity Opportunities Fund, LLC

Alta BioPharma Partners III, L.P.

Alta BioPharma Partners III GmbH & Co. Beteiligungs KG

Alta Embarcadero BioPharma Partners III, LLC

ONC General Partner Limited as General Partner of ONC Partners, L.P.