Exhibit 3, 4
                                                                    ------------

                            CERTIFICATE OF AMENDMENT
                                       OF
                           THIRD AMENDED AND RESTATED
                          CERTIFICATE OF INCORPORATION
                                       OF
                               CYTYC CORPORATION

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

     FIRST:   That the Board of Directors of the Corporation adopted resolutions
proposing and declaring advisable the following amendment to the Third Amended
and Restated Certificate of Incorporation of the Corporation:

              RESOLVED: That the first paragraph of Article FOURTH of the
Corporation's Third Amended and Restated Certificate of Incorporation shall be
amended to read in its entirety as follows:

              "FOURTH: The total number of shares of all classes of capital
stock which the Corporation shall have authority to issue is 205,000,000 shares,
consisting of 200,000,000 shares of common stock with a par value of $.01 per
share (the "Common Stock") and 5,000,000 shares of preferred stock with a par
value of $.01 per share (the "Preferred Stock")."

     SECOND:  The foregoing amendment to the Third Amended and Restated
Certificate of Incorporation of the Corporation was duly adopted by the
Stockholders of the Corporation in accordance with the applicable provisions of
Section 242 of the General Corporation Law of the State of Delaware.

     IN WITNESS WHEREOF, the Corporation has caused this Certificate of
Amendment to be executed by Patrick J. Sullivan, its President, this 19th day of
June, 2000.


                              /S/ Patrick J. Sullivan
                              -----------------------
                              Patrick J. Sullivan, President


                                      17