<PAGE>

                                                                   EXHIBIT 10.11


                          WARRANT EXERCISE AGREEMENT

     This Warrant Exercise Agreement (the "Agreement") is entered into as of
June ___, 2001 (the "Closing Date") by and among Data Race Inc. (doing business
                     ------------
as IP Axess), a Texas corporation, with headquarters located at 6509 Windcrest
Drive, Suite 120, Plano, Texas 75024 (the "Company"), and the warrant holders
                                           -------
listed on Schedule 1 attached hereto (individually, a "Holder" and collectively,
          ----------                                   ------
the "Holders").
     -------

     WHEREAS:

     A.   Some or all of Holders own and possess each of the following warrants
(the "Old Warrants") issued by the Company:  (1) warrants issued to certain of
      ------------
the Holders on June 25, 1999 and amended on March 2, 2001 which are exercisable
into that number of the Company's common stock, no par value per share (the
"Common Stock") in the respective amounts set forth opposite each Holder's name
 ------------
on Schedule 1 (the "Exercised Shares"), (2) warrants issued to certain of the
   ----------       ----------------
Holders on December 10, 1999 and amended on March 2, 2001 which are exercisable
into that number of Exercised Shares in the respective amounts set forth
opposite each Holder's name on Schedule 1 and (3) warrants issued to certain of
                               ----------
the Holders on June 12, 2000 which are exercisable into that number of Exercised
Shares in the respective amounts set forth opposite each Holder's name on
Schedule 1; and
----------

     B.   The Holders wish to exercise the Old Warrants upon the terms and
conditions stated in the Old Warrants as amended by this Agreement; and in
addition to such exercise of the Old Warrants, the Company desires to issue to
the Holders additional warrants, in substantially the same form attached hereto
as Exhibit A (the "New Warrants") to acquire 1,673,343 shares of Company Common
   ---------       ------------
Stock; and

     NOW THEREFORE, the Company and the Holders hereby agree as follows:

          1.  Amendment and Exercise of Old Warrants.  The parties agree that
              --------------------------------------
the Old Warrants are hereby amended by deleting Section 1(b)(xii) of each Old
Warrant in its entirety and replacing Section 1(b)(xii) of each Old Warrant with
the following:  ""Warrant Exercise Price" shall be $0.12 per common share,
subject to adjustment as hereinafter provided."  On the Closing Date, provided
that the provisions of Section 2 of this Agreement have been satisfied by the
Company, each Holder shall exercise its Old Warrants with respect to the
Exercised Shares (as set forth on Schedule 1 opposite each Holder's name) and
                                  ----------
each Holder shall pay to the Company on the Closing Date the Exercise Purchase
Price (as set forth on Schedule 1 opposite each Holder's name).  Within three
                       ----------
(3) business days following the Closing Date, the Company shall electronically
deliver to each Holder such Holder's Exercised Shares.  Each Holder covenants,
only on its own behalf, to the Company that such Holder shall sell the Exercised
Shares pursuant to an effective registration statement or an exemption from
registration under the Securities Act of 1933, as amended.  Each Holder
represents, only on its own behalf, to the Company that such Holder is an
"accredited investor" as that term is defined in Rule 501 of Regulation D.
<PAGE>

     2.   Conditions to Holders' Exercise.  The obligation of each Holder
          -------------------------------
hereunder to exercise its Old Warrants on the Closing Date is subject to the
satisfaction, at or before the Closing Date, of each of the following
conditions, provided that these conditions are for each Holder's sole benefit
and may be waived by such Holder at any time in its sole discretion by providing
the Company with prior written notice thereof:

          a.   The Company shall have executed and delivered to each Holder the
New Warrants (substantially in the form of Exhibit A), exercisable into that
                                           ---------
number of New Warrant Shares as set forth on Schedule 1 opposite such Holder's
                                             ----------
name;

          b.   The Company shall supplement or otherwise "sticker" the
prospectuses relating to the sale of the shares of Company Common Stock
underlying the Old Warrants under the Securities Act of 1933, as amended and
deliver the same to the Holders prior to the Closing Date;

          c.   The Company shall reimburse the Holders for the Holders' fees and
expenses (in an amount not to exceed $1,000.00) incurred by the Holders
concerning this Agreement and the consummation of the transactions contemplated
hereby; provided, however, that the Holders may elect, in their sole discretion,
        --------
to effect such reimbursement by deducting such costs and expenses from the
Exercise Purchase Price prior to making such payment to the Company; and

          d.   The Company shall have delivered to the Holders such other
documents relating to the transactions contemplated by this Agreement as the
Holders may reasonably request.



                          ***Signature Page Follows***

                                       2
<PAGE>

IN WITNESS WHEREOF, the Holders and the Company have caused this Warrant
Exercise Agreement to be duly executed as of the date first written above.

COMPANY:                                HOLDERS:

DATA RACE INC.                          CRANSHIRE CAPITAL, L.P.

By:                                     By:
   -------------------------------         -------------------------------
Name:                                   Name:
     -----------------------------           -----------------------------
Title:                                  Title:
      ----------------------------            ----------------------------

                                        EURAM CAP STRAT. "A" FUND LIMITED

                                        By:
                                           -------------------------------
                                        Name:
                                             -----------------------------
                                        Title:
                                              ----------------------------


                                        LIONHART INVESTMENTS LTD.

                                        By:
                                           -------------------------------
                                        Name:
                                             -----------------------------
                                        Title:
                                              ----------------------------


                                        KEYWAY INVESTMENTS LTD.

                                        By:
                                           -------------------------------
                                        Name:
                                             -----------------------------
                                        Title:
                                              ----------------------------

                                        ICN CAPITAL, LTD.

                                        By:
                                           -------------------------------
                                        Name:
                                             -----------------------------
                                        Title:
                                              ----------------------------

                                       3
<PAGE>

                                  SCHEDULE 1
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                                ***Attached***


                                       4
<PAGE>

                                   EXHIBIT A
                                   ---------
                              FORM OF NEW WARRANT
                              -------------------



                                ***Attached***

                                       5