SIGMATEL, INC. SECOND AMENDMENT TO SECOND AMENDED AND RESTATED INVESTORS RIGHTS AGREEMENT

Exhibit 10.6

SIGMATEL, INC.

SECOND AMENDMENT TO

SECOND AMENDED AND RESTATED INVESTORS’ RIGHTS AGREEMENT

This Second Amendment to Second Amended and Restated Investors’ Rights Agreement (this “Amendment”), is dated as of July 1, 2003. This Amendment amends that certain Second Amended and Restated Investors’ Rights Agreement dated as of August 15, 2000, by and among SigmaTel, Inc., a Texas corporation (the “Company”), and the signatories thereto and certain other Investors named therein, as previously amended by that certain First Amendment to Second Amended and Restated Investors’ Rights Agreement, dated November 17, 2000, by and among the Company and the signatories thereto (collectively, as amended, the “OriginalAgreement’). The Company and each of the signatories hereto may sign a separate signature page to this Amendment, all of which together shall constitute one instrument. All capitalized terms not otherwise herein defined shall have the meanings ascribed to them in the Original Agreement.

RECITALS

A. Of even date with this Amendment, the board of directors of Company has authorized and directed the officers of the Company to negotiate the terms of a proposed initial public offering (“Proposed IPO”) of the Company’s Common Stock, pursuant to which the Purchasers thereunder and the Company have agreed to execute this Amendment.

B. Section 1.1(g) of the Original Agreement currently defines an “IPO” as follows:

“the initial firm commitment underwritten offering of the Company’s Common Stock pursuant to a registration statement under the Act, with aggregate proceeds to the Company of at least $20 million at a public offering price of at least $5.00 per share (in the case of all classes and series of the Company’s stock other than the Series H Preferred Stock) or $7.50 per share (in the case of the Series H Preferred Stock only) (in any case, as adjusted for stock splits, stock dividends and like transactions.)”

C. The pricing range of the Proposed IPO currently anticipated by the Company and its underwriters will not be sufficient to meet the thresholds established in Section 1.1(g) of the Original Agreement in order for the Proposed IPO to meet the definition as an “IPO.” Thus, the Proposed IPO would not cause termination of certain rights and obligations under the Original Agreement, including, without limitation, the covenants of the Company set forth in Section 2 of the Original Agreement and the Investors’ right of first offer to purchase shares of the Company’s common stock pursuant to Section 3 of the Original Agreement.

D. The Company, its underwriters for the Proposed IPO, and the signatories hereto understand that the Proposed IPO will not occur unless certain rights and obligations under the Original Agreement, including without limitation those rights and obligations described in Recital C above, are terminated on the effective date of the Proposed IPO. Thus, the parties hereto wish to amend the Original Agreement to change the definition of “IPO” in Section 1.1(g)

of the Original Agreement so that the Proposed IPO will qualify as an “IPO” and thus cause the termination of certain rights and obligations under the Original Agreement, including without limitation those set forth in Section 2 and Section 3 thereof.

AGREEMENT

NOW THEREFORE, the Original Agreement is hereby amended as follows:

1. Amendment of Section 1.1(g) of the Original Agreement. Section 1.1(g) of the Original Agreement is hereby deleted in its entirety and the following is hereby inserted as Section 1.1(g) of the Original Agreement:

“(g) The term “IPO” means the initial firm commitment underwritten offering of the Company’s Common Stock pursuant to a registration statement under the Act, with aggregate proceeds to the Company of at least $50 million at a public offering price of at least $2.50 per share (as adjusted for stock splits, stock dividends and like transactions).”

2. Original Agreement Remains in Effect. Except as specifically provided above, the Original Agreement shall remain unmodified and in full force and effect.

3. Amendment. Pursuant to Section 4.7 of the Original Agreement, this Amendment has been approved by written agreement of (a) the Company, and (b) holders of two -thirds (2/3) of the Registrable Securities outstanding.

4. Governing Law. This Amendment shall be governed by and construed in accordance with the laws of the State of California.

(Signature Pages Follow)

2

IN WITNESS WHEREOF, this Amendment has been executed as of the date first written above.

COMPANY’S SIGNATURE PAGE TO SIGMATEL SECOND AMENDMENT TO

SECOND AMENDED AND RESTATED INVESTORS’ RIGHTS AGREEMENT

901 Mariner’s Island Blvd., #475

San Mateo, CA 94404

Attention: Ken Lawler

Facsimile: (650) 372-3930

INVESTORS’ SIGNATURE PAGE TO SIGMATEL SECOND AMENDMENT TO

SECOND AMENDED AND RESTATED INVESTORS’ RIGHTS AGREEMENT

INVESTORS’ SIGNATURE PAGE TO SIGMATEL SECOND AMENDMENT TO

SECOND AMENDED AND RESTATED INVESTORS’ RIGHTS AGREEMENT

INVESTORS’ SIGNATURE PAGE TO SIGMATEL SECOND AMENDMENT TO

SECOND AMENDED AND RESTATED INVESTORS’ RIGHTS AGREEMENT

INVESTORS’ SIGNATURE PAGE TO SIGMATEL SECOND AMENDMENT TO

SECOND AMENDED AND RESTATED INVESTORS’ RIGHTS AGREEMENT