Document:

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                                                                   Exhibit 10.12

                                 WARRANT

THE SECURITIES REPRESENTED BY THIS WARRANT HAVE NOT BEEN REGISTERED UNDER THE
SECURITIES ACT OF 1933, AS AMENDED, OR APPLICABLE STATE SECURITIES LAWS.  THE
SECURITIES HAVE BEEN ACQUIRED FOR INVESTMENT AND MAY NOT BE OFFERED FOR SALE,
SOLD, TRANSFERRED OR ASSIGNED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION
STATEMENT FOR THE SECURITIES UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE
"SECURITIES ACT"), OR APPLICABLE STATE SECURITIES LAWS, OR AN OPINION OF COUNSEL
IN FORM, REASONABLY ACCEPTABLE TO THE ISSUER THAT REGISTRATION IS NOT REQUIRED
UNDER THE SECURITIES ACT OR UNLESS SOLD PURSUANT TO RULE 144 UNDER SAID ACT.
ANY SUCH OFFER, SALE, ASSIGNMENT OR TRANSFER MUST ALSO COMPLY WITH THE
APPLICABLE STATE SECURITIES LAWS.

                                DATA RACE INC.

                       Warrant To Purchase Common Stock

Warrant No.:   ________                       Number of Shares:_______
Date of Issuance:  June ___, 2001

Data Race Inc., a Texas corporation, doing business as IP Axess (the "Company"),
                                                                      -------
hereby certifies that, for Ten United States Dollars ($10.00) and other good and
valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, ______________________, the registered holder hereof or its
permitted assigns, is entitled, subject to the terms set forth below, to
purchase from the Company upon surrender of this Warrant, at any time or times
on or after the date hereof, but not after 11:59 P.M. Central Time on the
Expiration Date (as defined herein) ______________________________________
________________(______) fully paid nonassessable shares of Common Stock (as
defined herein) of the Company (the "Warrant Shares") at the purchase price per
                                     --------------
share provided in Section 1(b) below.

     Section 1.

          (a) Warrant Exercise Agreement.  This Warrant is one of the Warrants
              --------------------------
(the "Warrants") issued pursuant to the terms of that certain Warrant Exercise
      --------
Agreement dated as of June ___, 2001, among the Company and the Holders referred
to therein (the "Warrant Exercise Agreement").
                 --------------------------

          (b) Definitions.  The following words and terms as used in this
              -----------
Warrant shall have the following meanings:
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          (i) "Common Stock" means (i) the Company's common stock, no par value
               ------------
per share, and (ii) any capital stock into which such Common Stock shall have
been changed or any capital stock resulting from a reclassification of such
Common Stock.

          (ii) "Exempt Issuance" means (A) a loan from a commercial bank which
                ---------------
has only an incidental equity feature, (B) any transaction involving the
Company's issuances of securities (1) as consideration in a merger or
consolidation, (2) in connection with a strategic partnership or joint venture
(the primary purpose of which is not to raise equity capital), or (3) as
consideration for the acquisition of a business, product, license or other
assets by the Company, (C) the issuance of common stock in a firm commitment,
underwritten public offering, (D) the issuance of securities upon exercise or
conversion of the Company's options, warrants or other convertible securities
outstanding as of the date hereof, (E) the grant of additional options or
warrants, or the issuance of additional securities, under any Company stock
option plan, restricted stock plan,  stock purchase plan or other plan or
written compensation agreement for the benefit of the Company's employees,
directors, consultants or advisors, or (F) the issuance of securities pursuant
to any shareholder rights plan adopted by the Company prior to the Closing Date
(as defined in the Warrant Exercise Agreement).

          (iii)  "Expiration Date" means the date five (5) years from the date
                  ---------------
of this Warrant 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.

          (iv) "Person" means an individual, a limited liability company, a
                ------
partnership, a joint venture, a corporation, a trust, an unincorporated
organization and a government or any department or agency thereof.

          (v) "Principal Market" means the Nasdaq National Market.
               ----------------

          (vi) "Securities Act" means the Securities Act of 1933, as amended.
                --------------

          (vii) "Warrant" means this Warrant and all Warrants issued in
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exchange, transfer or replacement of any thereof.

          (viii) "Warrant Exercise Price" shall be $0.25 per common share,
                  ----------------------
subject to adjustment as hereinafter provided.

     Section 2.  Exercise of Warrant.
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          (a) Subject to the terms and conditions hereof, this Warrant may be
exercised by the holder hereof then registered on the books of the Company, in
whole or in part, at any time on any day the Principal Market is open for
business (a "Business Day") on or after the opening of business on the date
             ------------
hereof and prior to 11:59 P.M. Central Time on the Expiration Date by (i)
delivery of a written notice, in the form of the subscription notice attached as
Exhibit A hereto (the "Exercise Notice"), of such holder's election to exercise
---------              ---------------
this Warrant, which notice shall specify the number of Warrant Shares to be
purchased, (ii) payment to the Company of an amount equal to the Warrant
Exercise Price multiplied by the number of Warrant Shares as to which this
Warrant is being exercised (plus any applicable issue or transfer taxes) (the
"Aggregate Exercise Price") in cash or by check or wire transfer, and (iii) the
-------------------------
surrender to a common carrier for delivery to the Company as soon as practicable
following such date, this Warrant (or an indemnification undertaking with
respect to this Warrant in the case of its loss, theft or destruction);
provided, that if such Warrant Shares are to be issued in any name other than
that of the registered holder of this Warrant, such issuance shall be deemed a
transfer and the provisions of Section 7 shall be applicable.  In the event of
any exercise of the rights represented by this Warrant in compliance with this
Section 2(a), a certificate or certificates for the Warrant Shares so purchased,
in such denominations as may be requested by the holder hereof and registered in
the name of, or as directed by, the holder, shall be delivered at the Company's
expense to, or as directed by, such holder as soon as practicable, and in no
event later than two Business Days, after the Company's receipt of the Exercise
Notice, the Aggregate Exercise Price and this Warrant (or an indemnification
undertaking with respect to this Warrant in the case of its loss, theft or
destruction).  Upon delivery of the Exercise Notice and Aggregate Exercise Price
referred to in clause (ii) above, the holder of this Warrant shall be deemed for
all corporate purposes to have become the holder of record of the Warrant Shares
with respect to which this Warrant has been exercised, irrespective of the date
of delivery of this Warrant as required by clause (iii) above or the
certificates evidencing such Warrant Shares.

          (b) Unless the rights represented by this Warrant shall have expired
or shall have been fully exercised, the Company shall, as soon as practicable
and in no event later than five (5) Business Days after any exercise and at its
own expense, issue a new Warrant identical in all respects to this Warrant
exercised except it shall represent rights to purchase the number of Warrant
Shares purchasable immediately prior to such exercise under this Warrant
exercised, less the number of Warrant Shares with respect to which such Warrant
is exercised.

          (c) No fractional shares of Common Stock are to be issued upon the
exercise of this Warrant, but rather the number of shares of Common Stock issued
upon exercise of this Warrant shall be rounded up or down to the nearest whole
number.

          (d) If the Company shall fail for any reason or for no reason to issue
to the holder on a timely basis as described in this Section 2, a certificate
for the number of shares of Common Stock to which the holder is entitled upon
the holder's exercise of this Warrant or a new Warrant for the number of shares
of Common Stock to which such holder is entitled pursuant to Section 2(b)
hereof, the Company shall, in addition to any other remedies under this Warrant
or otherwise available to such holder, pay as additional damages in cash to such
holder on each day the issuance

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<PAGE>

of such Common Stock certificate or new Warrant, as the case may be, is not
timely effected an amount equal to .25% of the product of (A) the sum of the
number of shares of Common Stock not issued to the holder on a timely basis and
to which the holder is entitled and/or, the number of shares represented by the
portion of this Warrant which is not being converted, as the case may be, and
(B) the average of the closing bid price of the Common Stock for the three
consecutive trading days immediately preceding the last possible date which the
Company could have issued such Common Stock or Warrant, as the case may be, to
the holder without violating this Section 2.

          (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 9.9% 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  9.9% 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 (the "1934 Act").  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 9.9% 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.

     Section 3.  Covenants as to Common Stock.  The Company hereby covenants and
                 ----------------------------
agrees as follows:

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<PAGE>

          (a) This Warrant is, and any Warrant issued in substitution for or
replacement of this Warrant will upon issuance be, duly authorized and validly
issued.

          (b) All Warrant Shares which may be issued upon the exercise of the
rights represented by this Warrant will, upon issuance, be validly issued, fully
paid and nonassessable and free from all taxes, liens and charges with respect
to the issue thereof.

          (c) During the period within which the rights represented by this
Warrant may be exercised, the Company will at all times have authorized and
reserved at least 100% of the number of shares of Common Stock needed to provide
for the exercise of the rights then represented by this Warrant and the par
value of said shares will at all times be less than or equal to the applicable
Warrant Exercise Price.

          (d) The Company shall promptly secure the listing of the shares of
Common Stock issuable upon exercise of this Warrant upon each national
securities exchange or automated quotation system, if any, upon which shares of
Common Stock are then listed (subject to official notice of issuance upon
exercise of this Warrant) and shall maintain, so long as any other shares of
Common Stock shall be so listed, such listing of all shares of Common Stock from
time to time issuable upon the exercise of this Warrant; and the Company shall
so list on each national securities exchange or automated quotation system, as
the case may be, and shall maintain such listing of, any other shares of capital
stock of the Company issuable upon the exercise of this Warrant if and so long
as any shares of the same class shall be listed on such national securities
exchange or automated quotation system.

          (e) The Company will not, by amendment of its Articles of
Incorporation or through any reorganization, transfer of assets, consolidation,
merger, dissolution, issue or sale of securities, or any other voluntary action,
avoid or seek to avoid the observance or performance of any of the terms to be
observed or performed by it hereunder, but will at all times in good faith
assist in the carrying out of all the provisions of this Warrant and in the
taking of all such action as may reasonably be requested by the holder of this
Warrant in order to protect the exercise privilege of the holder of this Warrant
against dilution or other impairment, consistent with the tenor and purpose of
this Warrant will take all such actions as may be necessary or appropriate in
order that the Company may validly and legally issue fully paid and
nonassessable shares of Common Stock upon the exercise of this Warrant.

          (f) Registration of Warrant Shares.
              ------------------------------

              (i) The Company shall prepare, and, as soon as practicable but
in no event later than thirty (30) calendar days after the date of issuance of
this Warrant, file with the Securities and Exchange Commission (the "SEC") a
                                                                     ---
Registration Statement(s) (the "Registration
                                ------------

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<PAGE>

Statement") on Form S-3 (or if such form is unavailable, such other form as is
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available for registration) covering the resale of all of the Warrant Shares and
any shares of capital stock issued or issuable with respect to this Warrant or
the Warrant Shares (the "Registrable Securities").  The initial Registration
                         ----------------------
Statement prepared pursuant hereto shall register for resale at least that
number of Company common stock shares equal to the number of Registrable
Securities as of the date immediately preceding the date the Registration
Statement is initially filed with the SEC. The Company shall use its best
efforts to have the Registration Statement declared effective by the SEC as soon
as practicable, but in no event later than ninety (90) calendar days after the
date of issuance of this Warrant.

          (ii) The Company shall promptly prepare and file with the SEC a
Registration Statement with respect to the Registrable Securities (on or prior
to the thirtieth (30th) calendar day after the date of issuance of this Warrant
for the registration of Registrable Securities pursuant to Section 3(f)(i)) and
use its best efforts to cause such Registration Statement relating to the
Registrable Securities to become effective as soon as possible after such filing
(but in no event later than the ninetieth (90th) calendar day after the date of
issuance of this Warrant for the registration of Registrable Securities pursuant
to Section 3(f)(i), and keep such Registration Statement effective pursuant to
Rule 415, promulgated under the Securities Act at all times until the earlier of
(i) the date as of which the Holder may sell all of the Registrable Securities
without restriction pursuant to Rule 144(k) promulgated under the Securities Act
(or successor thereto) or (ii) the date on which the Holder shall have sold all
the Registrable Securities (the "Registration Period"), which Registration
                                 -------------------
Statement (including any amendments or supplements thereto and prospectuses
contained therein) shall not contain any untrue statement of a material fact or
omit to state a material fact required to be stated therein, or necessary to
make the statements therein, in light of the circumstances in which they were
made, not misleading.

          (iii)  The Company shall prepare and file with the SEC such amendments
(including post-effective amendments) and supplements to a Registration
Statement and the prospectus used in connection with such Registration
Statement, which prospectus is to be filed pursuant to Rule 424 promulgated
under the Securities Act, as may be necessary to keep such Registration
Statement effective at all times during the Registration Period, and, during
such period, comply with the provisions of the Securities Act with respect to
the disposition of all Registrable Securities of the Company covered by such
Registration Statement until such time as all of such Registrable Securities
shall have been disposed of in accordance with the intended methods of
disposition by the seller or sellers thereof as set forth in such Registration
Statement.

          (iv) The Company shall use reasonable efforts to (i) register and
qualify the Registrable Securities covered by a Registration Statement under
such other securities or "blue sky" laws of such jurisdictions in the United
States as legal counsel to the Holder or the Holder reasonably requests, (ii)
prepare and file in those jurisdictions, such amendments (including post-
effective amendments) and supplements to such registrations and qualifications
as may be necessary to maintain the effectiveness thereof during the
Registration Period, (iii) take such other actions as may be necessary to
maintain such registrations and qualifications in effect at all times during the
Registration Period, and (iv) take all other actions reasonably necessary or
advisable to qualify the Registrable Securities for sale in such jurisdictions;
provided, however, that the Company shall not

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be required in connection therewith or as a condition thereto to (x) qualify to
do business in any jurisdiction where it would not otherwise be required to
qualify but for this Section 3(f)(iv), (y) subject itself to general taxation in
any such jurisdiction, or (z) file a general consent to service of process in
any such jurisdiction. The Company shall promptly notify the Holder of the
receipt by the Company of any notification with respect to the suspension of the
registration or qualification of any of the Registrable Securities for sale
under the securities or "blue sky" laws of any jurisdiction in the United States
or its receipt of actual notice of the initiation or threatening of any
proceeding for such purpose.

          (v) The Company shall use its best efforts either to (i) cause all the
Registrable Securities covered by a Registration Statement to be listed on each
securities exchange on which securities of the same class or series issued by
the Company are then listed, if any, if the listing of such Registrable
Securities is then permitted under the rules of such exchange, or (ii) secure
designation and quotation of all the Registrable Securities covered by the
Registration Statement on the Nasdaq National Market.  The Company shall pay all
fees and expenses in connection with satisfying its obligation under this
Section 3(f)(v).

          (vi) The Company shall otherwise use its best efforts to comply with
all applicable rules and regulations of the SEC in connection with any
registration hereunder and the Company shall use its best efforts to file with
the SEC in a timely manner all reports and documents required of the Company
under the Securities Act and the 1934 Act.

          (vii)  The Company shall take all other reasonable actions necessary
to expedite and facilitate disposition by the Holder of Registrable Securities
pursuant to a Registration Statement.

          (viii)  In the event any Registrable Securities are included in a
Registration Statement as required by this Section 3(f):

                  A.  To the fullest extent permitted by law, the Company will,
and hereby does, indemnify, hold harmless and defend the Holder, the directors,
officers, partners, employees, agents, representatives of, and the person or
entity, if any, who controls the Holder within the meaning of the Securities Act
or the 1934 Act, and any underwriter (as defined in the Securities Act) for the
Holder, and the directors and officers of, and each such person, if any, who
controls, any such underwriter within the meaning of the Securities Act or the
1934 Act (each, an "Indemnified Person"), against any losses, claims, damages,
                    ------------------
liabilities, judgments, fines, penalties, charges, costs, reasonable attorneys'
fees, amounts paid in settlement or expenses, joint or several, (collectively,
"Claims") incurred in investigating, preparing or defending any action, claim,
 ------
suit, inquiry, proceeding, investigation or appeal taken from the foregoing by
or before any court or governmental, administrative or other regulatory agency,
body or the SEC, whether pending or threatened, whether or not an indemnified
party is or may be a party thereto ("Indemnified Damages"), to which any of them
                                     -------------------
may become subject insofar as such Claims (or actions or proceedings, whether
commenced or threatened, in respect thereof) arise out of or are based upon: (i)
any untrue statement or alleged untrue statement of a material fact in a
Registration Statement or any post-effective amendment thereto or in any filing
made in connection with the qualification of the offering under the securities

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<PAGE>

or other "blue sky" laws of any jurisdiction in which Registrable Securities are
offered ("Blue Sky Filing"), or the omission or alleged omission to state a
          ---------------
material fact required to be stated therein or necessary to make the statements
therein not misleading, (ii) any untrue statement or alleged untrue statement of
a material fact contained in any preliminary prospectus if used prior to the
effective date of such Registration Statement, or contained in the final
prospectus (as amended or supplemented, if the Company files any amendment
thereof or supplement thereto with the SEC) or the omission or alleged omission
to state therein any material fact necessary to make the statements made
therein, in light of the circumstances under which the statements therein were
made, not misleading, (iii) any violation or alleged violation by the Company of
the Securities Act, the 1934 Act, any other law, including, without limitation,
any state securities law, or any rule or regulation thereunder relating to the
offer or sale of the Registrable Securities pursuant to a Registration Statement
(the matters in the foregoing clauses (i) through (iii) being, collectively,
"Violations").  The Company shall reimburse the Holder and each such underwriter
-----------
or controlling person, promptly as such expenses are incurred and are due and
payable, for any reasonable legal fees or other reasonable expenses incurred by
them in connection with investigating or defending any such Claim.
Notwithstanding anything to the contrary contained herein, the indemnification
agreement contained in this Section 3(f)(viii): (i) shall not apply to a Claim
by an Indemnified Person arising out of or based upon a Violation which occurs
in reliance upon and in conformity with information furnished in writing to the
Company by such Indemnified Person or underwriter for such Indemnified Person
expressly for use in connection with the preparation of the Registration
Statement or any such amendment thereof or supplement thereto, if such
prospectus was timely made available by the Company pursuant to this Section
3(f); (ii) with respect to any preliminary prospectus, shall not inure to the
benefit of any such person from whom the person asserting any such Claim
purchased the Registrable Securities that are the subject thereof (or to the
benefit of any person controlling such person) if the untrue statement or
omission of material fact contained in the preliminary prospectus was corrected
in the prospectus, as then amended or supplemented, if such prospectus was
timely made available by the Company pursuant to this Section 3(f), and the
Indemnified Person was promptly advised in writing not to use the incorrect
prospectus prior to the use giving rise to a violation and such Indemnified
Person, notwithstanding such advice, used it; (iii) shall not be available to
the extent such Claim is based on a failure of the Holder to deliver or to cause
to be delivered the prospectus made available by the Company, if such prospectus
was timely made available by the Company pursuant to this Section 3(f); and (iv)
shall not apply to amounts paid in settlement of any Claim if such settlement is
effected without the prior written consent of the Company, which consent shall
not be unreasonably withheld.  Such indemnity shall remain in full force and
effect regardless of any investigation made by or on behalf of the Indemnified
Person and shall survive the transfer of the Registrable Securities by the
Holder.

          (ix) The Company agrees that the Holder will suffer damages if the
Company fails to fulfill any of its obligations under this Section 3 (each such
event referred to herein as a "Registration Default") and that it would not be
                               --------------------
possible to ascertain the extent of such damages.  Accordingly, in the event of
such Registration Default, the Company hereby agrees to pay liquidated damages
("Liquidated Damages") by issuing to the Holder a warrant (substantially in the
  ------------------
form of this Warrant with the same Warrant Exercise Price and five (5) year
term) exercisable into that number of Company common shares equal to an amount
determined by multiplying (i) two

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percent (2%) of the Warrant Shares underlying this Warrant, by (ii) the
percentage derived by dividing (A) the actual number of days elapsed from the
last day of the date of the Registration Default or the prior 30-day period, as
applicable, to the day such Registration Default has been completely cured by
(B) 30. Any warrants required to be issued by the Company pursuant to this
Section 3(f)(ix) shall be issued within five (5) Business Days from the end of
each calendar month commencing on the first calendar month in which the
Registration Default occurs. In addition, the common shares underlying such
warrants issued as Liquidated Damages shall also be considered Registrable
Securities and shall have the registration rights set forth in this Warrant.

     Section 4.  Taxes.  The Company shall pay any and all taxes which may be
                 -----
payable with respect to the issuance and delivery of Warrant Shares upon
exercise of this Warrant.

     Section 5.  Warrant Holder Not Deemed a Stockholder.  Except as otherwise
                 ---------------------------------------
specifically provided herein, no holder, as such, of this Warrant shall be
entitled to vote or receive dividends or be deemed the holder of shares of the
Company for any purpose, nor shall anything contained in this Warrant be
construed to confer upon the holder hereof, as such, any of the rights of a
stockholder of the Company or any right to vote, give or withhold consent to any
corporate action (whether any reorganization, issue of stock, reclassification
of stock, consolidation, merger, conveyance or otherwise), receive notice of
meetings, receive dividends or subscription rights, or otherwise, prior to the
issuance to the holder of this Warrant of the Warrant Shares which he or she is
then entitled to receive upon the due exercise of this Warrant.  In addition,
nothing contained in this Warrant shall be construed as imposing any liabilities
on such holder to purchase any securities (upon exercise of this Warrant or
otherwise) or as a stockholder of the Company, whether such liabilities are
asserted by the Company or by creditors of the Company.  Notwithstanding this
Section 5, the Company will provide the holder of this Warrant with copies of
the same notices and other information given to the stockholders of the Company
generally, contemporaneously with the giving thereof to the stockholders.

     Section 6.  Representations of Holder.  The holder of this Warrant, by the
                 -------------------------
acceptance hereof, represents that it is acquiring this Warrant and the Warrant
Shares for its own account for investment only and not with a view towards, or
for resale in connection with, the public sale or distribution of this Warrant
or the Warrant Shares, except pursuant to sales registered or exempted under the
Securities Act; provided, however, that by making the representations herein,
the holder does not agree to hold this Warrant or any of the Warrant Shares for
any minimum or other specific term and reserves the right to dispose of this
Warrant and the Warrant Shares at any time in accordance with or pursuant to a
registration statement or an exemption under the Securities Act.  The holder of
this Warrant further represents, by acceptance hereof, that, as of this date,
such holder is an  "accredited investor" as such term is defined in Rule 501(a)
of Regulation D promulgated by the Securities and Exchange Commission under the
Securities Act (an "Accredited Investor").
                    -------------------

     Section 7.  Ownership and Transfer.
                 ----------------------

                                       9
<PAGE>

          (a) The Company shall maintain at its principal executive offices (or
such other office or agency of the Company as it may designate by notice to the
holder hereof), a register for this Warrant, in which the Company shall record
the name and address of the person in whose name this Warrant has been issued,
as well as the name and address of each transferee.  The Company may treat the
person in whose name any Warrant is registered on the register as the owner and
holder thereof for all purposes, notwithstanding any notice to the contrary, but
in all events recognizing any transfers made in accordance with the terms of
this Warrant.

          (b) This Warrant and the rights granted to the holder hereof are
transferable, in whole or in part, upon surrender of this Warrant, together with
a properly executed warrant power in the form of Exhibit B attached hereto;
provided, however, that any transfer or assignment shall be subject to the
conditions set forth in Section 7(c) below.

          (c) The holder of this Warrant understands that this Warrant has not
been and is not expected to be, registered under the Securities Act or any state
securities laws, and may not be offered for sale, sold, assigned or transferred
unless (a) subsequently registered thereunder, or (b) such holder shall have
delivered to the Company an opinion of counsel, in generally acceptable form, to
the effect that the securities to be sold, assigned or transferred may be sold,
assigned or transferred pursuant to an exemption from such registration;
provided that (i) any sale of such securities made in reliance on Rule 144
promulgated under the Securities Act may be made only in accordance with the
terms of said Rule and further, if said Rule is not applicable, any resale of
such securities under circumstances in which the seller (or the person through
whom the sale is made) may be deemed to be an underwriter (as that term is
defined in the Securities Act) may require compliance with some other exemption
under the Securities Act or the rules and regulations of the Securities and
Exchange Commission thereunder; and (ii) neither the Company nor any other
person is under any obligation to register the Warrants under the Securities Act
or any state securities laws or to comply with the terms and conditions of any
exemption thereunder.

          Section 8.  Adjustment of Warrant Exercise Price and Number of Shares.
                      ---------------------------------------------------------

          (a) Adjustment to Warrant Exercise Price and Number of Warrant Shares.
              -----------------------------------------------------------------
If the Company shall, at any time or from time to time, issue Company common
stock or instruments convertible or exercisable into Company common stock (other
than an Exempt Issuance) at a price per common stock share, a  conversion price
per common stock share or an exercise price per common stock share less than the
Warrant Exercise Price (such lesser price shall be deemed the "Differential
                                                               ------------
Price"), then immediately after such issue or sale the Warrant Exercise Price
-----
then in effect shall be reduced to the Differential Price.  Upon each such
adjustment of the Warrant Exercise

                                       10
<PAGE>

Price hereunder, the number of shares of Common Stock acquirable upon exercise
of this Warrant shall be adjusted to the number of shares determined by
multiplying the Warrant Exercise Price in effect immediately prior to such
adjustment by the number of shares of Common Stock acquirable upon exercise of
this Warrant immediately prior to such adjustment and dividing the product
thereof by the Differential Price.

          (b)  Notices.
               -------

              (i) Immediately upon any adjustment of the Warrant Exercise
Price, the Company will give written notice thereof to the holder of this
Warrant, setting forth in reasonable detail, and certifying, the calculation of
such adjustment.

              (ii) The Company will give written notice to the holder of this
Warrant at least twenty (20) days prior to the date on which the Company closes
its books or takes a record (A) with respect to any dividend or distribution
upon the Common Stock, (B) with respect to any pro rata subscription offer to
holders of Common Stock or (C) for determining rights to vote with respect to
any Organic Change (as defined below), dissolution or liquidation, provided that
such information shall be made known to the public prior to or in conjunction
with such notice being provided to such holder.

              (iii)  The Company will also give written notice to the holder of
this Warrant at least twenty (20) days prior to the date on which any Organic
Change, dissolution or liquidation will take place, provided that such
information shall be made known to the public prior to or in conjunction with
such notice being provided to such holder.

     Section 9.  Purchase Rights; Reorganization, Reclassification,
                 --------------------------------------------------
Consolidation, Merger or Sale.
-----------------------------

          (a) If at any time after the date hereof, the Company grants, issues
or sells any options, convertible securities or rights to purchase stock,
warrants, securities or other property pro rata to the record holders of any
class of Common Stock (the "Purchase Rights"), then the holder of this Warrant
                            ---------------
will be entitled to acquire, upon the terms applicable to such Purchase Rights,
the aggregate Purchase Rights which such holder could have acquired if such
holder had held the number of shares of Common Stock acquirable upon complete
exercise of this Warrant immediately before the date on which a record is taken
for the grant, issuance or sale of such Purchase Rights, or, if no such record
is taken, the date as of which the record holders of Common Stock are to be
determined for the grant, issue or sale of such Purchase Rights.

          (b) Any recapitalization, reorganization, reclassification,
consolidation, merger, sale of all or substantially all of the Company's assets
to another Person or other transaction which is effected in such a way that
holders of Common Stock are entitled to receive (either directly or upon
subsequent liquidation) stock, securities or assets with respect to or in
exchange for Common Stock is referred to herein as "Organic Change."  Prior to
                                                    --------------
the consummation of any (i) sale of all

                                       11
<PAGE>

or substantially all of the Company's assets to an acquiring Person or (ii)
other Organic Change following which the Company is not a surviving entity, the
Company will use its best efforts to secure from the Person purchasing such
assets or the successor resulting from such Organic Change (in each case, the
"Acquiring Entity") written agreement (in form and substance satisfactory to
 ----------------
the holders of Warrants representing a majority of the shares of Common Stock
obtainable upon exercise of the Warrants then outstanding) to deliver to each
holder of Warrants in exchange for such Warrants, a security of the Acquiring
Entity evidenced by a written instrument substantially similar in form and
substance to this Warrant and satisfactory to the holders of the Warrants
(including, an adjusted warrant exercise price equal to the value for the Common
Stock reflected by the terms of such consolidation, merger or sale, and
exercisable for a corresponding number of shares of Common Stock acquirable and
receivable upon exercise of the Warrants, if the value so reflected is less than
the Warrant Exercise Price in effect immediately prior to such consolidation,
merger or sale). Prior to the consummation of any other Organic Change, the
Company shall use its best efforts to make appropriate provision (in form and
substance satisfactory to the holders of Warrants representing a majority of the
shares of Common Stock obtainable upon exercise of the Warrants then
outstanding) to insure that each of the holders of the Warrants will thereafter
have the right to acquire and receive in lieu of or in addition to (as the case
may be) the shares of Common Stock immediately theretofore acquirable and
receivable upon the exercise of such holder's Warrants, such shares of stock,
securities or assets that would have been issued or payable in such Organic
Change with respect to or in exchange for the number of shares of Common Stock
which would have been acquirable and receivable upon the exercise of such
holder's Warrant as of the date of such Organic Change (without taking into
account any limitations or restrictions on the exerciseability of this Warrant).

          (c) In the event the Company proposes to effect an Organic Change,
then in addition to any other rights the holder may have, the holder shall have
the right to effect a Cashless Exercise (as defined below), by presentation and
surrender of this Warrant to the Company at its principal executive offices with
a written notice of the holder's intention to effect a Cashless Exercise,
including a calculation of the number of shares of Common Stock to be issued
upon such exercise in accordance with the terms hereof.  A "Cashless Exercise"
                                                            -----------------
shall mean that, in lieu of paying the Warrant Exercise Price in cash, the
holder shall surrender this Warrant for that number of Warrant Shares determined
by subtracting from the number of Warrant Shares otherwise issuable to the
holder upon such exercise, an amount of Warrant Shares (the "Surrendered
                                                             -----------
Shares") having a closing bid price (as reported by Bloomberg) on the date
------
immediately preceding the date of the exercise notice equal to the Aggregate
Exercise Price (as defined in Section 2) of the Warrant Shares for which this
Warrant is being exercised; and thereafter the Surrendered Shares shall no
longer be available for issuance hereunder.

     Section 10.  Lost, Stolen, Mutilated or Destroyed Warrant.  If this Warrant
                  --------------------------------------------
is lost, stolen, mutilated or destroyed, the Company shall, on receipt of an
indemnification undertaking, issue a new Warrant of like denomination and tenor
as this Warrant so lost, stolen, mutilated or destroyed.

                                       12
<PAGE>

     Section 11.  Notice.  Any notices, consents, waivers or other
                  ------
communications required or permitted to be given under the terms of this Warrant
must be in writing and will be deemed to have been delivered:  (i) upon receipt,
when delivered personally; (ii) upon receipt, when sent by facsimile (provided
confirmation of transmission is mechanically  or electronically generated and
kept on file by the sending party); or (iii) one Business Day after deposit with
a nationally recognized overnight delivery service, in each case properly
addressed to the party to receive the same.  The addresses and facsimile numbers
for such communications shall be:

          If to the Company:

                  Data Race Inc.
                  6509 Windcrest Drive, Suite 120
                  Plano, Texas 75024
                  Telephone:    (972) 205-4005
                  Facsimile:    (210) 558-0356
                  Attention:    Jim Scogin

          With copy to:

                  Jackson Walker LLP
                  901 Main Street, Suite 6000
                  Dallas, Texas 75202
                  Telephone:     (214) 953 - 5801
                  Facsimile:     (214) 953 - 5736
                  Attention:     Jim Ryan, Esq.

If to a holder of this Warrant, to it at the address and facsimile number set
forth on the Company's books and records, with copies to such holder's
representatives as set forth on the Company's books and records, or at such
other address and facsimile as shall be delivered to the Company upon the
issuance or transfer of this Warrant.  Each party shall provide five days' prior
written notice to the other party of any change in address or facsimile number.
Written confirmation of receipt (A) given by the recipient of such notice,
consent, waiver or other communication, (B) mechanically or electronically
generated by the sender's facsimile machine containing the time, date, recipient
facsimile number and an image of the first page of such transmission or (C)
provided by a nationally recognized overnight delivery service shall be
rebuttable evidence of personal service, receipt by facsimile or receipt from a
nationally recognized overnight delivery service in accordance with clause (i),
(ii) or (iii) above, respectively.

     Section 12.  [Omitted.]

     Section 13.  Date.  The date of this Warrant is June ___, 2001.  This
                  ----
Warrant, in all events, shall be wholly void and of no effect after the close of
business on the Expiration Date, except that notwithstanding any other
provisions hereof, the provisions of Section 7 shall continue in full force

                                       13
<PAGE>

and effect after such date as to any Warrant Shares or other securities issued
upon the exercise of this Warrant.

     Section 14.  Amendment and Waiver.  Except as otherwise provided herein,
                  --------------------
the provisions of the Warrants may be amended and the Company may take any
action herein prohibited, or omit to perform any act herein required to be
performed by it, only if the Company has obtained the written consent of the
holders of Warrants representing a majority of the shares of Common Stock
obtainable upon exercise of the Warrants then outstanding; provided that no such
action may increase the Warrant Exercise Price of the Warrants or decrease the
number of shares or class of stock obtainable upon exercise of any Warrants
without the written consent of the holder of such Warrant.

     Section 15.  Descriptive Headings; Governing Law.  The descriptive headings
                  -----------------------------------
of the several Sections and paragraphs of this Warrant are inserted for
convenience only and do not constitute a part of this Warrant.  This Warrant
shall be governed by the internal laws of the State of Illinois, without giving
effect to any choice of law or conflict of law provision or rule (whether of the
State of Illinois or any other jurisdictions) that would cause the application
of the laws of any jurisdictions other than the State of Illinois.

                                 [Signature Page Follows]

                                       14
<PAGE>

     This Warrant has been duly executed by the Company as of the date first set
forth above.

                                    DATA RACE INC.

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

<PAGE>

                              EXHIBIT A TO WARRANT
                              --------------------

                               SUBSCRIPTION FORM

        TO BE EXECUTED BY THE REGISTERED HOLDER TO EXERCISE THIS WARRANT

                                 DATA RACE INC.

     The undersigned holder hereby exercises the right to purchase
_________________ of the shares of Common Stock ("Warrant Shares") of Data Race
Inc., a Texas corporation (the "Company"), evidenced by the attached Warrant
(the "Warrant").  Capitalized terms used herein and not otherwise defined shall
have the respective meanings set forth in the Warrant.

     1.  Payment of Warrant Exercise Price.  The holder shall pay the sum of
$___________________ to the Company in accordance with the terms of the Warrant.

     2.  Delivery of Warrant Shares.  The Company shall deliver to the holder
__________ Warrant Shares in accordance with the terms of the Warrant.

Date:_______ ____, ______

Name of Registered Holder

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

<PAGE>

                              EXHIBIT B TO WARRANT
                              --------------------

                             FORM OF WARRANT POWER

FOR VALUE RECEIVED, the undersigned does hereby assign and transfer to
________________, Federal Identification No. __________, a warrant to purchase
____________ shares of the capital stock of Data Race Inc., a Texas corporation,
represented by warrant certificate no. _____, standing in the name of the
undersigned on the books of said corporation.  The undersigned does hereby
irrevocably constitute and appoint ______________, attorney to transfer the
warrants of said corporation, with full power of substitution in the premises.

Dated:  _________, 200_

                              --------------------------------

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

                                ***Attached***

                                       4
<PAGE>

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

                                ***Attached***

                                       5

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