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                                                                     EXHIBIT 3.1

                          AMENDMENT NO. 1 TO THE BYLAWS
                                       OF
                                CYBERONICS, INC.


         I, the undersigned President and Chief Executive Officer of Cyberonics,
Inc. (the "Corporation"), a corporation duly organized and existing under the
laws of the State of Delaware, hereby certify:

         That pursuant to Written Consent of the Board of Directors of the
Corporation dated March 21, 2001, the Board of Directors approved the amendment
of the Corporation's Bylaws as follows:

         A new section 8.13 shall be added to the Bylaws of the Corporation as
follows:

         8.13     Stock Options.

                  The corporation shall not grant any compensatory stock options
         with an exercise price that is less than 100% of the fair market value
         of the underlying common stock on the date of grant or reduce the
         exercise price of any compensatory stock option granted under any
         existing or future stock option plan, excluding the Employee Stock
         Purchase Plan, unless such option plan, grant or reduction in exercise
         price is approved by the holders of a majority of the shares present
         and entitled to vote at a duly convened meeting of the stockholders.
         This Section 8.13 of the bylaws may not be amended or repealed without
         the affirmative vote of the holders of a majority of the shares present
         and entitled to vote at a duly convened meeting of stockholders.

                                       CYBERONICS, INC.



                                       By:    /s/ Robert P. Cummins
                                          --------------------------------------
                                           Robert P. Cummins
                                           President and Chief Executive Officer

ATTEST:


By:   /s/ Reese S. Terry
  -----------------------------------
     Reese S. Terry
     Secretary