Ex-4.1 Amendment No. 2 to Rights Agreement dated as of November 1, 2007

Exhibit 4.1

AMENDMENT NO. 2 TO RIGHTS AGREEMENT

     This Amendment no. 2 to Rights Agreement is entered into as of November 1, 2007 (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 banking 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 (the “Rights Agreement”), as amended on May 23, 2005;

     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. 2 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 (e) of the Rights Agreement is hereby amended by deleting such section in its entirety and substituting therefore the following:

     A Person shall be deemed the “Beneficial Owner” of, and shall be deemed to “beneficially own,” any securities:

     (i) which such Person or any of such Person’s Affiliates or Associates, directly or indirectly, owns or has the right to acquire (whether such right is exercisable immediately, only after the passage of time, or after the occurrence of other events) pursuant to any agreement, arrangement or understanding (other than customary agreements with and between underwriters and selling group members with respect to a bona fide public offering of securities or agreements with or between Persons and the Company with respect to any other bona fide issuance of securities by the Company to such Persons for resale within 40 days, including without limitation pursuant to Section 4(2) of the Act or Rule 144A or Regulation S promulgated under the Act), whether or not in writing, or upon the exercise of conversion rights, exchange rights, other rights, warrants or options, or otherwise; provided, however, that a Person shall not be deemed the “Beneficial Owner” of, or to “beneficially own,” (A) securities tendered pursuant to a tender or exchange offer made by or on behalf of such Person or any of such Person’s Affiliates or Associates until such tendered securities are accepted for purchase or exchange, or (B) securities issuable upon exercise of Rights at any time prior to the occurrence of a Triggering Event, or (C) securities issuable upon exercise of Rights from and after the occurrence of a Triggering Event which Rights were acquired by such Person or any of such Person’s Affiliates or Associates prior to the Distribution Date or pursuant to Section 3(a) or Section 22 hereof (the “Original Rights”) or pursuant to Section 11(i) hereof in connection with an adjustment made with respect to any Original Rights;

     (ii) which such Person or any of such Person’s Affiliates or Associates, directly or indirectly, has the right to vote or dispose of or has “beneficial ownership” of (as determined pursuant to Rule 13d-3 of the General Rules and Regulations under the Exchange Act, or any comparable or successor rule), including pursuant to any agreement, arrangement or

understanding (other than customary agreements with and between underwriters and selling group members with respect to a bona fide public offering of securities or agreements with or between Persons and the Company with respect to any other bona fide issuance of securities by the Company to such Persons for resale within 40 days, including without limitation pursuant to Section 4(2) of the Act or Rule 144A or Regulation S promulgated under the Act), whether or not in writing; provided, however, that a Person shall not be deemed the “Beneficial Owner” of, or to “beneficially own,” any security under this subparagraph (ii) as a result of an agreement, arrangement or understanding to vote such security if such agreement, arrangement or understanding: (A) arises solely from a revocable proxy or consent given in response to a public proxy or consent solicitation made pursuant to, and in accordance with, the applicable provisions of the General Rules and Regulations under the Exchange Act, and (B) is not then reportable by such Person on Schedule 13D under the Exchange Act (or any comparable or successor report); or

     (iii) which are beneficially owned, directly or indirectly, by any other Person (or any Affiliate or Associate thereof) with which such Person (or any of such Person’s Affiliates or Associates) has any agreement, arrangement or understanding (other than customary agreements with and between underwriters and selling group members with respect to a bona fide public offering of securities or agreements with or between Persons and the Company with respect to any other bona fide issuance of securities by the Company to such Persons for resale within 40 days, including without limitation pursuant to Section 4(2) of the Act or Rule 144A or Regulation S promulgated under the Act) whether or not in writing, for the purpose of acquiring, holding, voting (except pursuant to a revocable proxy or consent as described in the proviso to subparagraph (ii) of this paragraph (e)) or disposing of any voting securities of the Company.

For all purposes of this Agreement, when making any calculation of the number of shares of Common Stock outstanding at any particular time, including for purposes of determining the particular percentage of such outstanding shares of Common Stock of which any Person is the Beneficial Owner, any securities not outstanding which are subject to options, warrants, rights or conversion privileges shall be deemed to be outstanding for the purpose of computing the percentage of outstanding securities of the class owned by such Person, including for purposes of determining the particular percentage of such outstanding shares of Common Stock of which any Person is the Beneficial Owner, but shall not be deemed to be outstanding for the purpose of computing the percentage of the class by any other Person.

     2. Section 1(r) of the Rights Agreement is hereby amended by deleting such section in its entirety and substituting therefore 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 21.0% 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 21.0%)), in which event each Person immediately shall cease to be an Exempted Person.

     3. Section 3(a) of the Rights Agreement is hereby amended by deleting such section in its entirety and substituting therefore the following:

“(a)

Until the earlier of (i) the close of business on the tenth Business Day (or such later date as may be determined by the Board) after the Stock Acquisition Date (or, if the tenth Business Day after the Stock Acquisition Date occurs before the Record Date, the close of business on the Record Date), or (ii) the close of business on the tenth Business Day (or such later date as may be determined by action of the Board) after the date that a tender or exchange offer (other than a Permitted Offer) by any Person (other than the Company, any Subsidiary of the Company, any employee benefit plan of the Company or of any Subsidiary of the Company, or any Person organized, appointed or established by the Company for or pursuant to the terms of any such plan) is first published or sent or given within the meaning of Rule 14d-2 of the General Rules and Regulations under the Exchange Act, if upon consummation thereof, such Person would be an Acquiring Person (the earlier of (i) and (ii) being herein referred to as the “Distribution Date”), (x) the Rights will be evidenced by the certificates for the Common Stock registered in the names of the holders of the Common Stock (which certificates for Common Stock shall be deemed also to be certificates for Rights) and not by separate certificates, and (y) the Rights will be transferable only in connection with the transfer of the underlying shares of Common Stock (including a transfer to the Company). As soon as practicable after the Distribution Date, the Rights Agent will send by first-class, insured, postage prepaid mail, to each record holder of the Common Stock as of the close of business on the Distribution Date, at the address of such holder shown on the records of the Company, one or more rights certificates, in substantially the form of Exhibit B hereto (the “Rights Certificates”), evidencing one Right for each share of Common Stock so held, subject to adjustment as provided herein. With respect to certificates for the Common Stock outstanding as of the close of business on the Record Date, until the Distribution Date, the Rights will be evidenced by such certificates for the Common Stock and the registered holders of the Common Stock shall also be the registered holders of the associated Rights. In addition, in connection with the issuance or sale of shares of Common Stock following the Distribution Date and prior to the redemption or expiration of the Rights, the Company (i) shall, with respect to shares of Common Stock so issued or sold pursuant to the exercise of stock options or under any employee benefit plan or arrangement, or upon the exercise, conversion or exchange of securities granted or issued by the Company prior to the Distribution Date, and (ii) may, in any other case, if deemed necessary or appropriate by the Board, issue Rights Certificates representing the appropriate number of Rights in connection with such issuance or sale; provided, however, that (x) no such Rights Certificate shall be issued if, and to the extent that, the Company shall be advised by counsel that such issuance would create a significant risk of material adverse tax consequences to the Company or the Person to whom such Rights Certificate would be issued, and (y) no such Rights Certificate shall be issued if, and to the extent that, appropriate adjustment shall otherwise have been made in lieu of the issuance thereof. In the event that an adjustment in the number of Rights per share of Common Stock has been made pursuant to Sections 11(i) or 11(p) hereof, at the time of distribution of the Rights Certificates, the Company shall make the necessary and appropriate rounding adjustments (in accordance with Section 14(a) hereof) so that Rights Certificates representing only whole numbers of Rights are distributed and cash is paid in lieu of any fractional Rights. As of and after the Distribution Date, the Rights will be evidenced solely by such Rights Certificates.

     4. 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, contain the entire agreement among the parties with respect to the subject matter thereof and amend, restate and supersede all prior and contemporaneous arrangements or understandings with respect thereto.

     5. 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.

     6. This Amendment shall be governed by the laws of the State of Delaware, exclusive of its choice of law and conflicts of law rules.

     7. 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.

[END OF TEXT]

     In Witness Whereof, the parties have duly executed this Amendment No. 2 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

Name: Dennis V. Moccia

President and Chief Executive Officer

Title: Managing Director