EX-4.1 Amendment No. 3 to Rights Agreement, dated as of June 2, 2008, between Aspect Medical Systems, Inc. and Computershare Trust Company, N.A

Exhibit 4.1

AMENDMENT NO. 3 TO RIGHTS AGREEMENT

     This Amendment No. 3 to Rights Agreement is entered into as of June 2, 2008 (the “Amendment”) by and between Aspect Medical Systems, Inc., a Delaware corporation (the “Company”) and Computershare Trust Company, N.A., formerly EquiServe Trust Company, N.A., a national bank association, as Rights Agent (the “Rights Agent”).

     Whereas, the Company and the Rights Agent are parties to that certain Rights Agreement dated November 29, 2004, as amended on May 23, 2005 and November 1, 2007 (the “Rights Agreement”);

     Whereas, the Rights (as defined in the Whereas clause at the beginning of the Rights Agreement) are still redeemable; and

     Whereas, the Company has directed the Rights Agent to enter into this Amendment No. 3 pursuant to Section 27 of the Rights Agreement;

     Now, Therefore, in consideration of the premises and mutual agreements set forth herein, the parties agree as follows:

     1.      Section 1(r) of the Rights Agreement is hereby amended by deleting such section in its entirety and substituting therefor the following:

               (r) “Exempted Person” shall mean any Person that would be deemed an Acquiring Person solely as a result of being the Beneficial Owner of shares of Common Stock issuable (but not yet issued) upon conversion or exchange of the Company’s 2.50% Convertible Senior Notes due 2014 (the “Notes”), unless and until such time as such Person, together with its Affiliates and Associates, directly or indirectly, becomes the Beneficial Owner of 25.0% or more of the shares of Common Stock then outstanding (other than under the circumstances described in the second sentence of Section 1(a) hereof (replacing for this purpose all references in Section 1(a) to 17.5% with 25.0%)), in which event such Person immediately shall cease to be an Exempted Person.

     2.      The Rights Agreement, as supplemented and modified by this Amendment, together with the other writings referred to in the Rights Agreement or delivered pursuant thereto which form a part thereof, contains the entire agreement among the parties with respect to the subject matter thereof and amends, restates and supersedes all prior and contemporaneous arrangements or understandings with respect thereto.

     3.      Upon the effectiveness of this Amendment, on and after the date hereof, each reference in the Rights Agreement to “this Agreement, “hereunder,” “hereof,” “herein” or words of like import, shall mean and be a reference to the Rights Agreement, as amended hereby. Except as specifically amended above, the Rights Agreement shall remain in full force and effect and is hereby ratified and confirmed.

     4.      This Amendment shall be governed by and construed in accordance with the laws of the State of Delaware applicable to contracts made and to be performed entirely within Delaware.

     5.     This Amendment may be executed in any number of counterparts, and each such counterpart shall be deemed to be an original instrument, but all such counterparts together shall constitute but one agreement.

     In Witness Whereof, the parties have duly executed this Amendment No. 3 to Rights Agreement, intending that it be executed under seal, as of the date first written above.

ASPECT MEDICAL SYSTEMS, INC.

COMPUTERSHARE TRUST COMPANY, N.A.,

AS RIGHTS AGENT

By:

/s/ Nassib Chamoun

By:

/s/ Dennis V. Moccia

Nassib Chamoun President and Chief Executive Officer

Dennis V. Moccia Managing Director