<PAGE>   1
                                                                   EXHIBIT 10.13

                  AMENDMENT NUMBER ONE TO EMPLOYMENT AGREEMENT

         This Amendment Number One is made and entered into this 6th day of
October, 2000 by and among ACCREDO HEALTH, INCORPORATED, a Delaware corporation
(the "Company") and DAVID D. STEVENS (the "Executive").

                                   WITNESSETH

         WHEREAS, the Company and Executive entered into an Employment Agreement
dated as of September 1, 1999; and

         WHEREAS, the parties now desire to make certain amendments to said
Employment Agreement as set forth below.

         NOW THEREFORE, for good and valuable consideration, the receipt and
adequacy of which is hereby acknowledged, the parties hereto agrees as follows:

         1.       Section 4.(a) of the Employment Agreement be and hereby is
                  amended to provide that effective September 1, 2000, the first
                  sentence thereof is deleted and the following sentence is
                  adopted in the place thereof:

                  As compensation for the performance by the Executive of the
                  services to be performed by the Executive hereunder during the
                  Employment Term, the Company shall pay the Executive a base
                  salary effective September 1, 2000 at the annual rate of Three
                  Hundred Eight Thousand Six Hundred Twenty-Nine and 00/100
                  ($308,629.00) Dollars (said amount being hereinafter referred
                  to as "Salary").

         2.       In order to reflect fiscal year 2001 bonus targets, Exhibit A
                  attached to and made a part of the Employment Agreement be and
                  hereby is amended by deleting Exhibit A in its present form
                  and substituting in the place thereof Exhibit A as attached to
                  this Amendment Number One.

         3.       Except as amended herein, all terms and conditions of the
                  Employment Agreement shall remaining in full force and effect.

         IN WITNESS WHEREOF, the Company and the Executive have duly executed
and delivered this Agreement as of the date and year first above written.

                                    ACCREDO HEALTH, INCORPORATED

                                    By:   /s/  Thomas W. Bell, Jr.
                                       ----------------------------------------

                                    Title:  Senior Vice President, Secretary
                                          -------------------------------------

                                              /s/ David D. Stevens
                                    -------------------------------------------
                                    DAVID D. STEVENS

<PAGE>   2

                                    EXHIBIT A
                         FISCAL YEAR 2001 BONUS TARGETS


TARGET Diluted EPS set by Board of Directors

<TABLE>
<CAPTION>
-------------------------------------------------------------------------------
                                           MAXIMUM INCENTIVE
          DILUTED EPS                      BONUS POTENTIAL(1)
-------------------------------------------------------------------------------
                                     75%                       100%
-------------------------------------------------------------------------------
    <S>                           <C>                         <C>
    TARGET less $.05                7.5%                        10%
-------------------------------------------------------------------------------
    TARGET less $.04               15.0%                        20%
-------------------------------------------------------------------------------
    TARGET less $.03               30.0%                        40%
-------------------------------------------------------------------------------
    TARGET less $.02               45.0%                        60%
-------------------------------------------------------------------------------
    TARGET less $.01               52.5%                        70%
-------------------------------------------------------------------------------
    TARGET                         60.0%                        80%
-------------------------------------------------------------------------------
    TARGET plus $.01               67.5%                        90%
-------------------------------------------------------------------------------
    TARGET plus $.02               75.0%                       100%
-------------------------------------------------------------------------------
</TABLE>

-----------------------
(1)      The 75% column applies to Joel Kimbrough, Thomas W. Bell, Jr., Kyle
         Callahan and John R. Grow.

         The 100% column applies to David D. Stevens.