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                                                                    EXHIBIT 10.5

                                 FIRST AMENDMENT

                                       TO

                  RIGHTS AGREEMENT DATED AS OF AUGUST 17, 1998

     This First Amendment dated June 28, 2001 (this "Amendment"), between
UroCor, Inc., a Delaware corporation (the "Company"), and American Stock
Transfer & Trust Company (the "Rights Agent"), amending the Rights Agreement
dated as of August 17, 1998 (the "Rights Agreement"), between the Company and
the Rights Agent.

     WHEREAS, the Company has entered into an Agreement and Plan of Merger dated
as of June 28, 2001 (the "Merger Agreement"), pursuant to which the Company will
merge (the "Merger") either into a wholly-owned subsidiary of, or into, Dianon
Systems, Inc., a Delaware corporation ("Dianon");

     WHEREAS, the Board of Directors of the Company has approved the Merger
Agreement and the Merger and has determined to amend the Rights Agreement so
that (i) Dianon and its Affiliates and Associates (as defined in the Rights
Agreement) shall not be deemed to be an Acquiring Person (as defined in the
Rights Agreement) and that no Distribution Date (as defined in the Rights
Agreement) shall occur as a result of the execution and delivery of the Merger
Agreement or the consummation of the Merger as contemplated thereby; and

     WHEREAS, the Board of Directors of the Company has determined to amend the
Rights Agreement in accordance with Section 27 thereof so that Sections 13 and
25(a)(iv) thereof shall not apply to the Merger as contemplated by the Merger
Agreement.

     NOW, THEREFORE, it is agreed as follows:

     1. Notwithstanding anything in the Rights Agreement to the contrary, (a)
     Dianon and its Affiliates and Associates shall not be deemed to be an
     Acquiring Person on account of the execution and delivery of the Merger
     Agreement or the announcement thereof or as a result of or arising out of
     the Merger; (b) no Distribution Date shall have occurred, shall occur or
     shall be deemed to occur as a result of the execution and delivery of the
     Merger Agreement or the announcement thereof or as a result of or arising
     out of the Merger; and (c) Sections 13 and 25(a)(iv) of the Rights
     Agreement shall not apply to the Merger.

     2. Except as amended or modified pursuant to this Amendment, the Rights
     Plan remains in full force and effect and this Amendment shall be subject
     to the terms thereof except as expressly modified hereby.


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Executed as of the date first written above.

                                            UROCOR, INC.

                                            By /s/ Michael W. George
                                               --------------------------------
                                            Name: Michael W. George
                                                 ------------------------------
                                            Title: President and CEO
                                                  -----------------------------



                                            AMERICAN STOCK TRANSFER & TRUST
                                            COMPANY, as Rights Agent

                                            By /s/ Herbert J. Lemmer
                                               --------------------------------
                                            Name: Herbert J. Lemmer
                                                 ------------------------------
                                            Title: Vice President
                                                  -----------------------------