<PAGE>

                                                                    EXHIBIT 10.6

                            [DATA RACE LETTERHEAD]


                                 March 2, 2001


Cranshire Capital, L.P. ("Cranshire")
                          ---------
Keyway Investments Ltd. ("Keyway")
                          ------
Lionhart Investments Ltd. ("Lionhart")
                            --------
c/o Strategic Investment Counsel, LLC
666 Dundee Road, Suite 1901
Northbrook, IL 60062
Attention: Anthony J. Ribaudo, Esq.

Re:  Amendments to Warrants Issued in June 1999

As you know, in connection with the June 1999 private placement of common stock
and warrants to Cranshire, Keyway and Lionhart (the "Investors"), on June 25,
                                                     ---------
1999, Data Race, Inc., a Texas corporation (the "Company") issued to the
                                                 -------
Investors warrants to purchase the Company's common stock (the "June 1999
                                                                ---------
Warrants").  The June 1999 Warrants consist entirely of the following:  (1)
--------
Warrant No. 1999-1 issued to Cranshire to purchase 213,296 shares of Company
common stock, (2) Warrant No. 1999-2 issued to Keyway to purchase 213,296 shares
of Company common stock and (3) Warrant No. 1999-3 issued to Lionhart to
purchase 213,296 shares of Company common stock.

In connection with the March 2001 private placement of the Company's common
stock and warrants to certain of the Investors, the Company has agreed to amend
certain terms of June 1999 Warrants as follows:

     1. Section 1(b)(v) of each June 1999 Warrant shall be deleted in its
  entirety and replaced with the following:  ""Expiration Date" means December
                                               ---------------
  10, 2003 or, if such date falls on a Saturday, Sunday or other day on which
  banks are required or authorized to be closed in the City of Chicago or the
  State of Illinois or on which trading does not take place on the principal
  exchange or automated quotation system on which the Common Stock is traded (a
  "Holiday"), the next date that is not a Holiday."

     2. Section 1(b)(xii) of each June 1999 Warrant shall be deleted in its
  entirety and replaced with the following:  ""Warrant Exercise Price" shall be
                                               ----------------------
  $0.9875 per common share, subject to adjustment as hereinafter provided."

                                       1
<PAGE>

     3.   A new section 2(e) shall be added to each June 1999 Warrant and shall
  read as follows:

          "(e)  Limitation on Beneficial Ownership.  The Company shall not
                ----------------------------------
     effect any exercise of this Warrant and no holder of this Warrant shall
     have the right to exercise this Warrant pursuant to Section 2 to the extent
     that after giving effect to such exercise such Person (together with such
     Person's affiliates) (A) would beneficially own in excess of 4.9% of the
     outstanding shares of the Common Stock following such exercise and (B)
     would have acquired, through exercise of this Warrant or otherwise, in
     excess of  4.9% of the outstanding shares of the Common Stock following
     such exercise during the 60-day period ending on and including such date of
     exercise.  For purposes of the foregoing sentence, the number of shares of
     Common Stock beneficially owned by a Person and its affiliates or acquired
     by a Person and its affiliates, as the case may be, shall include the
     number of shares of Common Stock issuable upon exercise of this Warrant
     with respect to which the determination of such sentence is being made, but
     shall exclude the number of shares of Common Stock which would be issuable
     upon (i) exercise of the remaining, non-exercised Warrant beneficially
     owned by such Person and its affiliates and (ii) exercise or conversion of
     the unexercised or unconverted portion of any other securities of the
     Company (including, without limitation, any warrants) subject to a
     limitation on conversion or exercise analogous to the limitation contained
     herein beneficially owned by such Person and its affiliates.  Except as set
     forth in the preceding sentence, for purposes of this Section 2(e),
     beneficial ownership shall be calculated in accordance with Section 13(d)
     of the Securities Exchange Act of 1934, as amended.  A holder of this
     Warrant may request the Company to waive the restrictions of this paragraph
     by providing prior written notice to the Company and the Company shall
     waive such restrictions of this paragraph and such waiver shall take effect
     on the sixty first (61st) calendar day following the Company's receipt of
     such written notice from the Holder to the Company.  Notwithstanding
     anything to the contrary contained herein, each Exercise Notice shall
     constitute a representation by the holder submitting such Exercise Notice
     that, after giving effect to such Exercise Notice, (A) the holder will not
     beneficially own (as determined in accordance with this Section 2(e)) and
     (B) during the 60-day period ending on and including such date of exercise,
     the holder will not have acquired, through exercise of this Warrant or
     otherwise, a number of shares of Common Stock in excess of 4.9% of the
     outstanding shares of Common Stock as reflected in the Company's most
     recent Form 10-Q or Form 10-K, as the case may be, or more recent public
     press release or other public notice by the Company setting forth the
     number of shares of Common Stock outstanding, but after giving effect to
     exercise of this Warrant by such holder since the date as of which such
     number of outstanding shares of Common Stock was reported."

                                       2
<PAGE>

If the foregoing is acceptable, please execute this letter below and return an
executed copy to the Company at the address above.

Very truly yours,

DATA RACE, INC.

By:  /s/ James G. Scogin
     ---------------------------------

Name:  James G. Scogin
       -------------------------------

Title:  Senior Vice President, CFO
        ------------------------------


AGREED AND ACCEPTED THIS
2nd DAY OF MARCH, 2001

INVESTORS (HOLDERS OF
JUNE 1999 WARRANTS):

CRANSHIRE CAPITAL, L.P.

By:  /s/ Mitchell P. Kopin
     ---------------------------------

Name:  Mitchell P. Kopin
       -------------------------------

Title:  President-Downsview Capital The General Partner
        -----------------------------------------------


KEYWAY INVESTMENTS LTD.

By:  /s/ Paul Moore
     ---------------------------------

Name:  Paul Moore
       -------------------------------

Title:  Director
        ------------------------------


LIONHART INVESTMENTS LTD.


By:  /s/ Terrence P. Duffy
     ---------------------------------

Name:  Terrence P. Duffy
       -------------------------------

Title:  Director
        ------------------------------

                                       3