Exhibit 3.1

                                                                          PAGE 1

                               State of Delaware

                        Office of the Secretary of State

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     I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO HEREBY

CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF AMENDMENT

OF "VISX, INCORPORATED", FILED IN THIS OFFICE ON THE THIRD DAY OF JUNE, A.D.

1999, AT 10 O'CLOCK A.M.

     A FILED COPY OF THIS CERTIFICATE HAS BEEN FORWARDED TO THE NEW CASTLE

COUNTY RECORDER OF DEEDS.





                                   /s/ Edward J. Freel
                                   ---------------------------------------------
                                   Edward J. Freel, Secretary of State

                               [SEAL OF DELAWARE]

2162938 8100                       AUTHENTICATION:   9784848

991222296                                    DATE:   06-04-99

                            CERTIFICATE OF AMENDMENT

                                       OF

                     RESTATED CERTIFICATE OF INCORPORATION

                                       OF

                               VISX, INCORPORATED

      VISX, INCORPORATED (the "Company"), a corporation organized and existing
under and by virtue of the General Corporation Law of the State of Delaware,
DOES HEREBY CERTIFY:

      FIRST: That at a meeting of the Board of Directors of the Company
resolutions were duly adopted setting forth a proposed amendment to the
Restated Certificate of Incorporation of said corporation, declaring said
amendment to be advisable and calling a meeting of the stockholders of said
corporation for consideration thereof. The resolution setting forth the
proposed amendment is as follows:

      RESOLVED, that the Restated Certificate of Incorporation of VISX,
Incorporated be amended by changing the fourth Article thereof so that, as
amended, said Article shall be and read as follows:

      "IV.  The total number of shares of all classes of stock that the
Company is authorized to issue is one hundred eighty million (180,000,000)
shares of Common Stock with a par value of $0.01 per share."

      SECOND: That thereafter, pursuant to resolution of its Board of
Directors, an annual meeting of the stockholders of said corporation was duly
called and held, upon notice in accordance with Section 222 of the General
Corporation Law of the State of Delaware at which meeting the necessary number
of shares as required by statute were voted in favor of the amendment.

      THIRD: That the aforesaid amendment was duly adopted in accordance with
the applicable provisions of Section 242 of the General Corporation Law of the
State of Delaware.

      IN WITNESS WHEREOF, said corporation has caused this certificate to be
signed by Mark B. Logan, its Chairman of the Board and Chief Executive Officer,
this 28th day of May, 1999.

                                       By: /s/ Mark B. Logan
                                           ------------------------------------
                                           Mark B. Logan
                                           Chairman of the Board and Chief
                                           Executive Officer