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Exhibit 3.1

SECOND AMENDMENT TO RIGHTS AGREEMENT

        This Second Amendment to Rights Agreement, dated as of October 15, 2005 (this "Second Amendment"), is entered into by and between Advanced Neuromodulation Systems, Inc., a Texas corporation (the "Company"), and Computershare Investor Services LLC ("Computershare" or "Rights Agent").

        WHEREAS, the Company (then known as Quest Medical, Inc.) and KeyCorp Shareholder Services, Inc., the predecessor of Computershare, are parties to that certain Rights Agreement dated as of August 30, 1996, as amended by the Amendment to Rights Agreement dated as of January 25, 2002 (as amended, the "Rights Agreement");

        WHEREAS, the Company proposes to enter into an Agreement and Plan of Merger (as the same may be amended or supplemented from time to time, the "Merger Agreement"), dated as of October 14, 2005, by and among St. Jude Medical, Inc, a Minnesota corporation ("Parent"), Apollo Merger Corp., a Texas corporation and a wholly owned subsidiary of Parent ("Sub"), and the Company, which provides for, among other things, a tender offer (the "Offer") by Sub or Parent to purchase all of the outstanding Common Stock (as defined in the Rights Agreement) of the Company followed by the merger of Sub with and into the Company (the "Merger");

        WHEREAS, pursuant to Section 29 of the Rights Agreement, (i) the Board of Directors of the Company has the exclusive power and authority to administer the Rights Agreement and to exercise all rights and powers specifically granted to the Board of Directors or to the Company, or as may be necessary or advisable in the administration of the Agreement, including, without limitation, a determination to amend the Rights Agreement and (ii) all actions, calculations, interpretations and determinations that are done or made by the Board of Directors of the Company in good faith are final, conclusive and binding on the Company, the Rights Agent, the holders of the Rights (as defined in the Rights Agreement), and all other parties, and shall not subject the Board of Directors of the Company to any liability to the holders of Rights;

        WHEREAS, by a Requisite Majority (as defined in the Rights Agreement), the Board of Directors of the Company has approved the Offer and the Merger and determined that the Offer and Merger, and the other transactions contemplated by the Merger Agreement, are Permitted Transactions (as defined in the Rights Agreement) within the meaning of Section 1(b)(l) of the Rights Agreement;

        WHEREAS, pursuant to Section 27 of the Rights Agreement, the Company, by action of its Board of Directors, and the Rights Agent may from time to time supplement or amend the Rights Agreement without the approval of any holders of Rights in order to make provisions in regard to matters or questions arising under the Rights Agreement that the Company and Rights Agent may deem necessary or desirable and that will be consistent with, and for the purpose of fulfilling, the objectives of the Board of Directors in adopting the Rights Agreement;

        WHEREAS, the Merger Agreement contemplates that the Company will amend the Rights Agreement to the extent necessary to provide that the execution and delivery of the Merger Agreement and the completion of the transactions contemplated by the Merger Agreement will not cause (i) the Rights to become exercisable under the Rights Agreement or (ii) Parent or Sub or any of their affiliates to be deemed an Acquiring Person (as defined in the Rights Agreement);

        WHEREAS, for the avoidance of doubt, the Board of Directors has determined that it is in the best interests of the Company and its shareholders to amend the Rights Agreement to exempt the Merger Agreement and the transactions contemplated by such agreement, including without limitation the Offer and the Merger, from the application of the Rights Agreement;

        NOW, THEREFORE, in consideration of the premises, the terms and provisions set forth herein, the mutual benefits to be gained by the performance thereof and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, and in accordance with

Section 27 of the Rights Agreement, the Company and the Rights Agent hereby amend the Rights Agreement as follows:

        1.     The definition of "Acquiring Person" in Section 1(b) of the Rights Agreement is hereby amended by adding the following sentence at the end thereof:

Notwithstanding anything in this Agreement to the contrary, none of St. Jude Medical, Inc, a Minnesota corporation ("Parent"), Sub (as defined in the Merger Agreement (as defined below)), or any of their Affiliates or Associates, shall be deemed to be an Acquiring Person by virtue of the execution, delivery or performance of the Agreement and Plan of Merger, dated as of October 14, 2005 (as the same may be amended from time to time, the "Merger Agreement"), among Parent, Sub and the Company, or the consummation of the transactions contemplated thereby, including, without limitation, the commencement of the Offer (as defined in the Merger Agreement), the acquisition of any shares of the Company's outstanding Common Stock pursuant to the terms of the Offer, the merger of Sub with and into the Company pursuant to the terms of the Merger Agreement (the "Merger") or the announcement of the foregoing transactions; it being understood that such transactions are Permitted Transactions for all purposes pursuant to this Agreement.

        2.     The definition of "Stock Acquisition Date" in Section 1(s) of the Rights Agreement is hereby amended by adding the following sentence at the end thereof:

Notwithstanding anything in this Agreement to the contrary, a Stock Acquisition Date shall not be deemed to have occurred as a result of the execution, delivery or performance of the Merger Agreement, or the consummation of the transactions contemplated thereby, including without limitation, the commencement of the Offer, the acquisition of any shares of the Company's outstanding Common Stock pursuant to the terms of the Offer or the Merger, or the announcement of the foregoing transactions, including the filing of any report pursuant to Section 13(d) under the Exchange Act.

        3.     Section 1(i) of the Rights Agreement is hereby amended by adding the following sentence at the end thereof:

Notwithstanding anything in this Agreement to the contrary, a Distribution Date shall not be deemed to have occurred as the result of the execution, delivery or performance of the Merger Agreement or the consummation of the transactions contemplated thereby, including, without limitation, the commencement of the Offer, the acquisition of any shares of the Company's outstanding Common Stock pursuant to the terms of the Offer or the Merger or the announcement of the foregoing transactions.

        4.     Section 7(a) of the Rights Agreement is hereby amended to change the reference to "August 30, 2011 (the "Final Expiration Date")," to "August 30, 2011 or, if earlier, immediately prior to the consummation of the Merger as contemplated by the Merger Agreement (the earlier of such dates, the "Final Expiration Date"),"

        5.     The Rights Agreement is hereby amended by adding a new Section 35 immediately after the end of Section 34 thereof to read in its entirety as follows:

Section 35. Merger Agreement with Parent and Related Transactions. Notwithstanding any other provision of this Agreement to the contrary, neither the approval, execution or delivery of the Merger Agreement nor the performance, consummation or announcement of the transactions contemplated by the Merger Agreement, is or shall be deemed to be a Section 11(a)(ii) Event or a Section 13 Event, nor will such approval, execution, delivery, performance, consummation or announcement result in the occurrence of a Stock Acquisition Date, a Distribution Date, a Triggering Event or any other event that causes a separation of

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the Rights from the underlying Common Stock, entitle or permit the holders of the Rights to exercise the Rights or otherwise affect the rights of the holders of Rights, including by giving the holders of the Rights the right to acquire securities of any party to the Merger Agreement.

        6.     This Second Amendment shall become effective as of the date of the Merger Agreement. If the Merger Agreement is terminated at any time prior to the Effective Time (as defined in the Merger Agreement), this Second Amendment shall be inapplicable to any events, acts or circumstances that occur or exist after such termination, provided, however, it shall remain effective with respect to the transactions contemplated by the Offer, the Merger and the Merger Agreement which have already been consummated as of such termination.

        7.     This Second Amendment shall be deemed to be a contract made under the laws of the State of Texas and for all purposes shall be governed by and construed in accordance with the laws of such State applicable to contracts to be made and performed entirely within such State.

        8.     This Second Amendment may be executed in any number of counterparts, each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.

        9.     In all respects not inconsistent with the terms and provisions of this Second Amendment, the Rights Agreement is hereby ratified, adopted, approved and confirmed. In executing and delivering this Second Amendment, the Rights Agent shall be entitled to all of the privileges and immunities afforded to the Right Agent under the terms and conditions of the Rights Agreement.

        10.   If any term, provision, covenant or restriction in this Second Amendment is held by a court of competent jurisdiction or other authority to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Second Amendment, and of the Rights Agreement, shall remain in full force and effect and shall in no way be affected, impaired or invalidated.

[signature page follows]

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        IN WITNESS WHEREOF, the parties hereto have caused this Second Amendment to be duly executed as of the date first above written.

ADVANCED NEUROMODULATION SYSTEMS, INC.
By:	/s/  CHRISTOPHER G. CHAVEZ
Name:  Christopher G. Chavez Title:    President and Chief Executive Officer
COMPUTERSHARE INVESTOR SERVICES LLC
By:	/s/  MARK ASBURY
Name:  Mark Asbury Title:    Relationship Manager

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Second Amendment to Rights Agreement dated as of October 15, 2005