<PAGE>
 
                                                                  EXHIBIT 10.6.1

                                Amendment No. 1

                          Dated as of July 1, 1998
                     to the Registration Rights Agreement

     This Amendment No. 1 (the "Amendment") to that certain Registration Rights 
Agreement (the "Registration Rights Agreement") dated February 14, 1996 between 
Fletcher Spaght, Inc., a Massachusetts corporation (the "Holder") and Nitinol 
Medical Technologies Inc., a Delaware corporation (the "Company"), is made as of
July 1, 1998. All capitalized terms used herein and not otherwise defined 
shall have the meanings ascribed to such terms in the Registration Rights 
Agreement.

                                   Recitals
                                   --------

     WHEREAS, pursuant to Section 1 of the Registration Rights Agreement, the 
Company granted to the Holder certain registrations rights for the Shares and
the Warrant Shares; and

     WHEREAS, the Holder wishes to transfer certain of the Warrants and the 
Holder and the Company wish to provide for the transfer of the registration 
rights with such Warrants.

     NOW THEREFORE, in consideration of the foregoing and for other good and
valuable consideration, receipt of which is hereby acknowledged, the parties
agree as follows:

     1.   Amendment to Section 5. Section 5 of the Registration Rights Agreement
          ----------------------
is hereby amended in its entirety to read as follows:
          
          "The Holder may assign its rights and obligations under this
     Registration Rights Agreement to any stockholder, employee or consultant of
     the Holder or to any employee of the Company to whom the Holder distributes
     the Registrable Securities."

     2.   Miscellaneous.
          -------------

          2.1  Governing Law. This Amendment shall be governed by, and construed
               -------------
and enforced in accordance with, the laws of the State of Delaware.

          2.2  Successors and Assigns. Except as otherwise provided herein, the 
               ----------------------
provisions hereof shall inure to the benefit of, and be binding upon the 
successors, assigns, heirs, executors and administrators of the parties hereto.

          2.3  Remaining Agreement. Except as amended hereby, the Registration 
               -------------------
Rights Agreement shall remain in full force and effect in all respects.

<PAGE>
 
          2.4  Counterparts. This Amendment may be execute in any number of 
               ------------
counterparts, each of which shall be an original, but all of which together
shall constitute one instrument.

     IN WITNESS WHEREOF, this Amendment No. 1 to the Registration Rights
Agreement is hereby executed as of the date first above written.


                                             NITINOL MEDICAL TECHNOLOGIES, INC.

                                             By: /s/ Thomas M. Tully
                                                -------------------------------
                                                Name:  Thomas M. Tully
                                                Title: President and Chief
                                                       Executive Officer


                                             FLETCHER SPAGHT, INC.

                                             By: /s/ R. John Fletcher
                                                -------------------------------
                                                Name:  R. John Fletcher
                                                Title: Chairman



                                      -2-