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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
                                                  -----------------------------<PAGE>   1

                                                                    EXHIBIT 10.6

                                  UROCOR, INC.

            1997 NON-EMPLOYEE DIRECTOR STOCK OPTION PLAN, AS AMENDED

1.       Purpose.

         This 1997 Non-Employee Director Stock Option Plan (this "Plan") of
UroCor, Inc., a Delaware corporation (the "Company"), is adopted, subject to
stockholder approval, for the benefit of the directors of the Company who at the
time of their service are not employees of the Company or any of its
subsidiaries ("Non-Employee Directors"), and is intended to advance the
interests of the Company by providing the Non-Employee Directors with additional
incentive to serve the Company by increasing their proprietary interest in the
success of the Company.

2.       Administration.

         This Plan shall be administered by a committee to be appointed by the
Board of Directors of the Company (the "Committee"), which Committee shall
consist of not less than two members of the Board of Directors and shall be
comprised solely of members of the Board of Directors who qualify as
non-employee directors as defined in Rule 16b-3(b)(3) of the Securities Exchange
Act of 1934, as amended (the "Securities Exchange Act"). For the purposes of
this Plan, a majority of the members of the Committee shall constitute a quorum
for the transaction of business, and the vote of a majority of those members
present at any meeting shall decide any question brought before that meeting. No
member of the Committee shall be liable for any act or omission of any other
member of the Committee or for any act or omission on his own part, including
(without limitation) the exercise of any power or discretion given to him under
this Plan, except those resulting from his own gross negligence or willful
misconduct. All questions of interpretation and application of this Plan, or as
to options granted hereunder (the "Options"), shall be subject to the
determination, which shall be final and binding, of a majority of the whole
Committee. Notwithstanding the above, the selection of Non-Employee Directors to
whom Options are to be granted, the number of shares subject to any Option, the
exercise price of any Option and the term of any Option shall be as hereinafter
provided and the Committee shall have no discretion as to such matters.

3.       Option Shares.

         The stock subject to the Options and other provisions of this Plan
shall be shares of the Company's Common Stock, $.01 par value per share (or such
other par value as may be designated by act of the Company's stockholders, the
"Common Stock"). The total amount of Common Stock with respect to which Options
may be granted shall not exceed 300,000 shares in the aggregate; provided, that
the class and aggregate number of shares which may be subject to the Options
granted hereunder shall be subject to adjustment in accordance with the
provisions of Paragraph 12 of this Plan. Such shares may be treasury shares or
authorized but unissued shares.

         If any outstanding Option for any reason shall expire or terminate by
reason of the death of the optionee or the fact that the optionee ceases to be a
director, the surrender of any such Option, or any other cause, the shares of
Common Stock allocable to the unexercised portion of such Option may again be
subject to an Option under this Plan.

4.       Grant of Options.

         (a) Current Directors. Subject to the provision of Section 16, for so
         long as this Plan is in effect and shares are available for the grant
         of Options hereunder, on July 1 of each year beginning July 1, 2000,
         there shall be granted to each person who is a Non-Employee Director on
         such July 1 an Option to purchase 7,500 shares of Common Stock at a per
         share Option Price equal to the fair market value of a share of the
         Company's Common Stock on such date (such number of shares being
         subject to the adjustments provided in Section 12 of this Plan).

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         (b) New Directors. Subject to the provisions of Section 16, for so long
         as this Plan is in effect and shares are available for the grant of
         Options hereunder, each person who shall become a Non-Employee Director
         after the effective date of this Plan shall be granted, on the date of
         his election, whether by the Stockholders or the Board of Directors in
         accordance with applicable law, an Option to purchase 10,000 shares of
         Common Stock at a per share Option Price equal to the fair market value
         of a share of Common Stock on such date (such number of shares being
         subject to the adjustments provided in Section 12 of this Plan).

         (c) Chairman of the Board of Directors. Subject to the provision of
         Section 16, for so long as this Plan is in effect and shares are
         available for the grant of Options hereunder, on July 1 of each year
         beginning July 1, 2000, there shall be granted to the person, if any,
         who is both a Non-Employee Director and the Chairman of the Board of
         Directors on such July 1, an Option to purchase 2,500 shares of Common
         Stock at a per share Option Price equal to the fair market value of a
         share of Common Stock on such date (such number of shares being subject
         to the adjustments provided in Section 12 of this Plan).

         (d) Fair Market Value. For purposes of this Section 4, the "fair market
         value" of a share of Common Stock as of any particular date shall mean
         (i) if the Common Stock is listed or admitted to trading on any
         securities exchange or on The National Association of Securities
         Dealers (the "NASD") Automated Quotation System ("Nasdaq") Stock
         Market's National Market, the closing price on such day on the
         principal securities exchange or on The Nasdaq Stock Market's National
         Market on which the Common Stock is traded or quoted, or if such day is
         not a trading day for such securities exchange or The Nasdaq Stock
         Market's National Market, the closing price on the first preceding day
         that was a trading day, (ii) if the Common Stock is not then listed or
         admitted to trading on any securities exchange or on The Nasdaq Stock
         Market's National Market, the closing bid price on such day as reported
         by the NASD, or if no such price is reported by the NASD for such day,
         the closing bid price as reported by the NASD on the first preceding
         day for which such price is available, and (iii) if the Common Stock is
         not then listed or admitted to trading on any securities exchange or on
         The Nasdaq Stock Market's National Market and no such closing bid price
         is reported by the NASD, as determined by another reputable quotation
         source selected by the Committee in good faith.

5.       Duration of Options.

         Each Option granted under this Plan shall be exercisable for a term of
nine years from the date such Option first becomes exercisable pursuant to
Section 6 hereof, subject to earlier termination as provided in Section 9 of
this Plan.

6.       Amount Exercisable.

         Each Option granted under this Plan may be exercised in whole or in
part at any time commencing one year after the grant thereof.

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7.       Exercise of Options.

         An optionee may exercise his Option by delivering to the Company a
written notice stating (a) that such optionee wishes to exercise such Option on
the date such notice is so delivered, (b) the number of shares of stock with
respect to which such Option is to be exercised and (c) the address to which the
certificate representing such shares of stock should be mailed. To be effective,
such written notice shall be accompanied by payment of the Option Price of each
of such shares of stock. Each such payment shall be made by cash, cashier's
check or bank draft drawn on a national banking association or postal or express
money order, payable to the order of the Company in United States dollars.

         As promptly as practicable after the receipt by the Company of (a) such
written notice from the optionee and (b) payment, in the form required by the
foregoing provisions of this Section 7, of the Option Price of the shares of
stock with respect to which such Option is to be exercised, a certificate
representing the number of shares of stock with respect to which such Option has
been so exercised registered in the name of such optionee, shall be delivered to
such optionee, provided that such delivery shall be considered to have been made
when such certificate shall have been mailed, postage prepaid, to such optionee
at the address specified for such purpose in such written notice from the
optionee to the Company.

8.       Transferability of Options.

         Options shall not be transferable by the optionee otherwise than by
will or under the laws of descent and distribution.

9.       Termination.

         Except as may be otherwise expressly provided in this Plan, each
Option, to the extent it shall not have been exercised previously, shall
terminate on the earlier of the following:

                  (a) At 5:00 p.m., Oklahoma City time, on the last day of the
         60-day period commencing on the date on which the optionee ceases to be
         a member of the Company's Board of Directors, for any reason other than
         the death or permanent disability of the optionee, during which period
         the optionee shall be entitled to exercise all Options held by the
         optionee on the date on which the optionee ceased to be a member of the
         Company's Board of Directors which could have been exercised on such
         date;

                  (b) On the last day of the one-year period commencing on the
         date of the optionee's death while serving as a member of the Company's
         Board of Directors, during which period the executor or administrator
         of the optionee's estate or the person or persons to whom the
         optionee's Option shall have been transferred by will or the laws of
         descent or distribution, shall be entitled to exercise all Options in
         respect of the number of shares that the optionee would have been
         entitled to purchase had the optionee exercised such Options on the
         date of his death; or

                  (c) Ten years after the date of grant of such Option.

10.      Requirements of Law.

         The Company shall not be required to sell or issue any shares under any
Option if the issuance of such shares shall constitute a violation by the
optionee or the Company of any provisions of any law or regulation of any
governmental authority. Each Option granted under this Plan shall be subject to
the requirements that, if at any time the Board of Directors of the Company or
the Committee shall determine that the listing, registration or qualification of
the shares subject thereto upon any securities exchange or under any state or
federal law of the United States or of any other country

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or governmental subdivision thereof, or the consent or approval of any
governmental regulatory body, or investment or other representations, are
necessary or desirable in connection with the issue or purchase of shares
subject thereto, no such Option may be exercised in whole or in part unless such
listing, registration, qualification, consent, approval or representation shall
have been effected or obtained free of any conditions not acceptable to the
Board of Directors. Any determination in this connection by the Committee shall
be final, binding and conclusive. If the shares issuable on exercise of an
Option are not registered under the Securities Act of 1933, as amended (the
"Securities Act"), the Company may imprint on the certificate for such shares
the following legend or any other legend which counsel for the Company considers
necessary or advisable to comply with the Securities Act:

         THE SHARES OF STOCK REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
         REGISTERED UNDER THE SECURITIES ACT OF 1933 OR UNDER THE SECURITIES
         LAWS OF ANY STATE AND MAY NOT BE SOLD OR TRANSFERRED EXCEPT UPON SUCH
         REGISTRATION OR UPON RECEIPT BY THE CORPORATION OF AN OPINION OF
         COUNSEL SATISFACTORY TO THE CORPORATION, IN FORM AND SUBSTANCE
         SATISFACTORY TO THE CORPORATION, THAT REGISTRATION IS NOT REQUIRED FOR
         SUCH SALE OR TRANSFER.

The Company may, but shall in no event be obligated to, register any securities
covered hereby pursuant to the Securities Act (as now in effect or as hereafter
amended) and, if any shares are so registered, the Company may remove any legend
on certificates representing such shares. The Company shall not be obligated to
take any other affirmative action to cause the exercise of an Option or the
issuance of shares pursuant thereto to comply with any law or regulation of any
governmental authority.

11.      No Rights as Stockholder.

         No optionee shall have rights as a stockholder with respect to shares
covered by his Option until the date of issuance of a stock certificate for such
shares; and, except as otherwise provided in Section 12 hereof, no adjustment
for dividends, or otherwise, shall be made if the record date therefor is prior
to the date of issuance of such certificate.

12.      Changes in the Company's Capital Structure.

         The existence of outstanding Options shall not affect in any way the
right or power of the Company or its stockholders to make or authorize any or
all adjustments, recapitalizations, reorganizations or other changes in the
Company's capital structure or its business, or any merger or consolidation of
the Company, or any issue of bonds, debentures, preferred or prior preference
stock ahead of or affecting the Common Stock or the rights thereof, or the
dissolution or liquidation of the Company, or any sale or transfer of all or any
part of its assets or business, or any other corporate act or proceeding,
whether of a similar character or otherwise.

         If the Company shall effect a subdivision or consolidation of shares or
other capital readjustment, the payment of a stock dividend or other increase or
reduction of the number of shares of Common Stock outstanding, without receiving
compensation therefor in money, services or property, then (a) the number, class
and per share price of shares of stock subject to outstanding Options hereunder
shall be appropriately adjusted in such a manner as to entitle an optionee to
receive upon exercise of an Option, for the same aggregate cash consideration,
the same total number and class or classes of shares as he would have received
had he exercised his Option in full immediately prior to the event requiring the
adjustment; and (b) the number and class of shares then reserved for issuance
under this Plan and the number of shares to be subject to the grants to be made
pursuant to Section 4 shall be adjusted by substituting for the total number and
class of shares of stock then reserved or subject to grant the number and class
or classes of shares of stock that would have been received by the owner of an
equal number of outstanding shares of Common Stock as the result of the event
requiring the adjustment, disregarding any fractional shares.

         If the Company merges or consolidates with another corporation, whether
or not the Company is a surviving corporation, or if the Company is liquidated
or sells or otherwise disposes of substantially all its assets while unexercised
Options remain outstanding under this Plan, or if any "person" (as that term is
used in Section 13(d) and 14(d)(2) of the Securities Exchange Act) is or becomes
the beneficial owner, directly or indirectly, of securities of the Company

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representing greater than 50% of the combined voting power of the Company's then
outstanding securities, after the effective date of such merger, consolidation,
liquidation, sale or other disposition, as the case may be, each holder of an
outstanding Option shall be entitled, upon exercise of such Option, to receive,
in lieu of shares of Common Stock, the number and class or classes of shares of
such stock or other securities or property to which such holder would have been
entitled if, immediately prior to such merger, consolidation, liquidation, sale
or other disposition, such holder had been the holder of record of a number of
shares of Common Stock equal to the number of shares as to which such Option may
be exercised.

         Except as otherwise expressly provided in this Plan, the issue by the
Company of shares of stock of any class, or securities convertible into shares
of stock of any class, for cash or property, or for labor or services either
upon direct sale or upon the exercise of rights or warrants to subscribe
therefor, or upon conversion of shares or obligations of the Company convertible
into such shares or other securities, shall not affect, and no adjustment by
reason thereof shall be made with respect to, the number or price of shares of
Common Stock then subject to outstanding Options.

13.      Amendment or Termination of Plan.

         The Board of Directors may modify, revise or terminate this Plan at any
time and from time to time; provided, however, that without the further approval
of the holders of at least a majority of the outstanding shares of voting stock,
or if the provisions of the corporate charter, bylaws or applicable state law
prescribes a greater degree of stockholder approval for this action, without the
degree of stockholder approval thus required, the Board of Directors may not (a)
materially increase the benefits accruing to participants under this Plan; (b)
materially increase the number of shares of Common Stock which may be issued
under this Plan; or (c) materially modify the requirements as to eligibility for
participation in this Plan, unless, in each such case, the Board of Directors of
the Company shall have obtained an opinion of legal counsel to the effect that
stockholder approval of the amendment is not required (x) by law, (y) by the
rules and regulations of, or any agreement with, the National Association of
Securities Dealers, Inc. or (z) to make available to the optionee with respect
to any option granted under this Plan, the benefits of Rule 16b-3 of the Rules
and Regulations under the Securities Exchange Act, or any similar or successor
rule. In addition, the provisions of this Plan may not be amended more than once
every six months other than to comport with changes in the Internal Revenue Code
of 1986, as amended, the Employee Retirement Income Security Act of 1974, as
amended, or the rules thereunder. All Options granted under this Plan shall be
subject to the terms and provisions of this Plan and any amendment, modification
or revision of this Plan shall be deemed to amend, modify or revise all Options
outstanding under this Plan at the time of such amendment, modification or
revision. If this Plan is terminated by action of the Board of Directors, all
outstanding Options may be terminated.

14.      Written Agreement.

         Each Option granted hereunder shall be embodied in a written option
agreement, which shall be subject to the terms and conditions prescribed above,
and shall be signed by the optionee and by the appropriate officer of the
Company for and in the name and on behalf of the Company. Such an option
agreement shall contain such other provisions as the Committee in its discretion
shall deem advisable.

15.      Indemnification of Committee and Board of Directors.

         The Company shall, to the fullest extent permitted by law, indemnify,
defend and hold harmless any person who at any time is a party or is threatened
to be made a party to any threatened, pending or completed action, suit or
proceeding (whether civil, criminal, administrative or investigative) in any way
relating to or arising out of this Plan or any Option or Options granted
hereunder by reason of the fact that such person is or was at any time a
director of the Company or a member of the Committee against judgments, fines,
penalties, settlements and reasonable expenses (including attorneys' fees)
actually incurred by such person in connection with such action, suit or
proceeding. This right of indemnification shall inure to the benefit of the
heirs, executors and administrators of each such person and is in

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addition to all other rights to which such person may be entitled by virtue of
the by-laws of the Company or as a matter of law, contract or otherwise.

16.      Effective Date of Plan.

         This Plan shall become effective, subject to stockholder approval, on
May 5, 1997. This Plan, and all Options granted under this Plan on or after May
5, 1997, and prior to stockholder approval, shall be void and of no further
force and effect unless this Plan shall have been approved by the requisite vote
of the stockholders entitled to vote at a meeting of the stockholders of the
Company called for such purpose prior to May 5, 1998.

         No Option shall be granted pursuant to this Plan on or after May 5,
2007.

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