<PAGE>   1
                                                                     EXHIBIT 4.3

         THIS WARRANT AND THE SHARES ISSUABLE UPON THE EXERCISE OF THIS WARRANT
         HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED.
         EXCEPT AS OTHERWISE SET FORTH HEREIN, NEITHER THIS WARRANT NOR ANY OF
         SUCH SHARES MAY BE SOLD, TRANSFERRED OR ASSIGNED IN THE ABSENCE OF AN
         EFFECTIVE REGISTRATION STATEMENT FOR SUCH SECURITIES UNDER SAID ACT OR,
         AN OPINION OF COUNSEL, IN FORM, SUBSTANCE AND SCOPE CUSTOMARY FOR
         OPINIONS OF COUNSEL IN COMPARABLE TRANSACTIONS, THAT REGISTRATION IS
         NOT REQUIRED UNDER SUCH ACT OR UNLESS SOLD PURSUANT TO RULE 144 UNDER
         SUCH ACT.

                                                                   Right to
                                                                   Purchase
                                                                   25,000 Shares
                                                                   of Common
                                                                   Stock, par
                                                                   value $0.01
                                                                   per share


                             STOCK PURCHASE WARRANT

                  THIS CERTIFIES THAT, for value received, Daniel M. Carney or
his registered assigns, is entitled to purchase from T-NETIX, Inc., a Colorado
corporation (the "Company"), at any time or from time to time during the period
specified in Paragraph 2 hereof, twenty-five thousand (25,000) fully paid and
nonassessable shares of the Company's common stock, par value $0.01 per share
(the "Common Stock"), at an exercise price of $6.05 per share (the "Exercise
Price"). The term "Warrant Shares," as used herein, refers to the shares of
Common Stock purchasable hereunder. The Warrant Shares and the Exercise Price
are subject to adjustment as provided in Paragraph 4 hereof.

                  This Warrant is subject to the following terms, provisions,
and conditions:

                  1. MANNER OF EXERCISE; ISSUANCE OF CERTIFICATES; PAYMENT FOR
SHARES. Subject to the provisions hereof, this Warrant may be exercised by the
holder hereof, in whole or in part, by the surrender of this Warrant, together
with a completed exercise agreement in the form attached hereto (the "Exercise
Agreement"), to the Company during normal business hours on any trading day at
the Company's principal executive offices (or such other office or agency of the
Company as it may designate by notice to the holder hereof), and upon (i)
payment to the Company in cash, by certified or official bank check or by wire
transfer for the account of the Company of the Exercise Price for the Warrant
Shares specified in the Exercise Agreement or (ii) if the resale of the Warrant
Shares by the holder is not then registered pursuant to an effective
registration statement under the Securities Act of 1933, as amended (the
"Securities Act"), delivery to the Company of a written notice of an election to
effect a "Cashless Exercise" (as defined in Section 11(c) below) for the Warrant
Shares specified in the Exercise Agreement. The



<PAGE>   2

Warrant Shares so purchased shall be deemed to be issued to the holder hereof or
such holder's designee, as the record owner of such shares, as of the close of
business on the date on which this Warrant shall have been surrendered, the
completed Exercise Agreement shall have been delivered, and payment shall have
been made for such shares (or an election to effect a Cashless Exercise has been
made) as set forth above. Certificates for the Warrant Shares so purchased,
representing the aggregate number of shares specified in the Exercise Agreement,
shall be delivered to the holder hereof within a reasonable time, not exceeding
two (2) trading days, after this Warrant shall have been so exercised. The
certificates so delivered shall be in such denominations as may be requested by
the holder hereof and shall be registered in the name of such holder or such
other name as shall be designated by such holder. If this Warrant shall have
been exercised only in part, then, unless this Warrant has expired, the Company
shall, at its expense, at the time of delivery of such certificates, deliver to
the holder a new Warrant representing the number of shares with respect to which
this Warrant shall not then have been exercised.

                  2. PERIOD OF EXERCISE. This Warrant is exercisable at any time
or from time to time on or after the date on which this Warrant is issued and
delivered pursuant to the terms of the Securities Purchase Agreement (the "Issue
Date") and before 5:00 p.m., New York City time, on the fifth (5th) anniversary
of the Issue Date (the "Exercise Period").

                  3. CERTAIN AGREEMENTS OF THE COMPANY. The Company hereby
covenants and agrees as follows:

                           (a) SHARES TO BE FULLY PAID. All Warrant Shares will,
upon issuance in accordance with the terms of this Warrant, be validly issued,
fully paid, and nonassessable and free from all taxes, liens, and charges with
respect to the issue thereof.

                           (b) RESERVATION OF SHARES. During the Exercise
Period, the Company shall at all times have authorized, and reserved for the
purpose of issuance upon exercise of this Warrant, a sufficient number of shares
of Common Stock to provide for the exercise of this Warrant.

                           (c) LISTING. The Company shall promptly secure the
listing of the shares of Common Stock issuable upon exercise of the 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.



                                      -2-
<PAGE>   3

                           (d) CERTAIN ACTIONS PROHIBITED. The Company will not,
by amendment of its charter 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. Without limiting the generality of the foregoing, the
Company (i) will not increase the par value of any shares of Common Stock
receivable upon the exercise of this Warrant above the Exercise Price then in
effect, and (ii) 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.

                           (e) SUCCESSORS AND ASSIGNS. This Warrant will be
binding upon any entity succeeding to the Company by merger, consolidation, or
acquisition of all or substantially all the Company's assets.

                  4. ANTIDILUTION PROVISIONS. During the Exercise Period, the
Exercise Price and the number of Warrant Shares shall be subject to adjustment
from time to time as provided in this Paragraph 4.

                  In the event that any adjustment of the Exercise Price as
required herein results in a fraction of a cent, such Exercise Price shall be
rounded up to the nearest cent.

                           (a) ADJUSTMENT OF EXERCISE PRICE AND NUMBER OF SHARES
UPON ISSUANCE OF COMMON STOCK. Except as otherwise provided in Paragraphs 4(c)
and 4(e) hereof, if and whenever on or after the Issue Date of this Warrant, the
Company issues or sells, or in accordance with Paragraph 4(b) hereof is deemed
to have issued or sold, any shares of Common Stock for no consideration or for a
consideration per share (before deduction of reasonable expenses or commissions
or underwriting discounts or allowances in connection therewith) less than the
Market Price (as hereinafter defined) on the date of issuance (or deemed
issuance) of such Common Stock (a "Dilutive Issuance"), then immediately upon
the Dilutive Issuance, the Exercise Price will be reduced to a price determined
by multiplying the Exercise Price in effect immediately prior to the Dilutive
Issuance by a fraction, (i) the numerator of which is an amount equal to the sum
of (x) the number of shares of Common Stock actually outstanding immediately
prior to the Dilutive Issuance, plus (y) the quotient of the aggregate
consideration, calculated as set forth in Paragraph 4(b) hereof, received by the
Company upon such Dilutive Issuance divided by the Market Price in effect
immediately prior to the Dilutive Issuance, and (ii) the denominator of which is
the total number of shares of Common Stock Deemed Outstanding (as defined below)
immediately after the Dilutive Issuance.



                                      -3-
<PAGE>   4

                           (b) EFFECT ON EXERCISE PRICE OF CERTAIN EVENTS. For
purposes of determining the adjusted Exercise Price under Paragraph 4(a) hereof,
the following will be applicable:

                                    (i) ISSUANCE OF RIGHTS OR OPTIONS. If the
Company in any manner (except in replacement of or exchange for warrants, rights
or options of a target company in a merger or acquisition) issues or grants any
warrants, rights or options, whether or not immediately exercisable, to
subscribe for or to purchase Common Stock or other securities convertible into
or exchangeable for Common Stock ("Convertible Securities") (such warrants,
rights and options to purchase Common Stock or Convertible Securities are
hereinafter referred to as "Options") and the price per share for which Common
Stock is issuable upon the exercise of such Options is less than the Market
Price on the date of issuance or grant of such Options, then the maximum total
number of shares of Common Stock issuable upon the exercise of all such Options
will, as of the date of the issuance or grant of such Options, be deemed to be
outstanding and to have been issued and sold by the Company for such price per
share. For purposes of the preceding sentence, the "price per share for which
Common Stock is issuable upon the exercise of such Options" is determined by
dividing (i) the total amount, if any, received or receivable by the Company as
consideration for the issuance or granting of all such Options, plus the minimum
aggregate amount of additional consideration, if any, payable to the Company
upon the exercise of all such Options, plus, in the case of Convertible
Securities issuable upon the exercise of such Options, the minimum aggregate
amount of additional consideration payable upon the conversion or exchange
thereof at the time such Convertible Securities first become convertible or
exchangeable, by (ii) the maximum total number of shares of Common Stock
issuable upon the exercise of all such Options (assuming full conversion of
Convertible Securities, if applicable). No further adjustment to the Exercise
Price will be made upon the actual issuance of such Common Stock upon the
exercise of such Options or upon the conversion or exchange of Convertible
Securities issuable upon exercise of such Options.

                                    (ii) ISSUANCE OF CONVERTIBLE SECURITIES. If
the Company in any manner issues or sells any Convertible Securities, whether or
not immediately convertible (other than where the same are issuable upon the
exercise of Options) and the price per share for which Common Stock is issuable
upon such conversion or exchange is less than the Market Price on the date of
issuance of such Convertible Securities, then the maximum total number of shares
of Common Stock issuable upon the conversion or exchange of all such Convertible
Securities will, as of the date of the issuance of such Convertible Securities,
be deemed to be outstanding and to have been issued and sold by the Company for
such price per share. For the purposes of the preceding sentence, the "price per
share for which Common Stock is issuable upon such conversion or exchange" is
determined by dividing (i) the total amount, if any, received or receivable by
the Company as consideration for the issuance or sale of all such Convertible
Securities, plus the minimum aggregate amount of additional consideration, if
any, payable to the Company upon the conversion or exchange thereof at the time
such Convertible Securities first become convertible or exchangeable, by (ii)
the maximum total number of shares of Common Stock issuable upon the conversion
or exchange of all such Convertible Securities. No further



                                      -4-
<PAGE>   5

adjustment to the Exercise Price will be made upon the actual issuance of such
Common Stock upon conversion or exchange of such Convertible Securities.

                                    (iii) CHANGE IN OPTION PRICE OR CONVERSION
RATE. If there is a change at any time in (i) the amount of additional
consideration payable to the Company upon the exercise of any Options; (ii) the
amount of additional consideration, if any, payable to the Company upon the
conversion or exchange of any Convertible Securities; or (iii) the rate at which
any Convertible Securities are convertible into or exchangeable for Common Stock
(other than under or by reason of provisions designed to protect against
dilution), the Exercise Price in effect at the time of such change will be
readjusted to the Exercise Price which would have been in effect at such time
had such Options or Convertible Securities still outstanding provided for such
changed additional consideration or changed conversion rate, as the case may be,
at the time initially granted, issued or sold.

                                    (iv) TREATMENT OF EXPIRED OPTIONS AND
UNEXERCISED CONVERTIBLE SECURITIES. If, in any case, the total number of shares
of Common Stock issuable upon exercise of any Option or upon conversion or
exchange of any Convertible Securities is not, in fact, issued and the rights to
exercise such Option or to convert or exchange such Convertible Securities shall
have expired or terminated, the Exercise Price then in effect will be readjusted
to the Exercise Price which would have been in effect at the time of such
expiration or termination had such Option or Convertible Securities, to the
extent outstanding immediately prior to such expiration or termination (other
than in respect of the actual number of shares of Common Stock issued upon
exercise or conversion thereof), never been issued.

                                    (v) CALCULATION OF CONSIDERATION RECEIVED.
If any Common Stock, Options or Convertible Securities are issued, granted or
sold for cash, the consideration received therefor for purposes of this Warrant
will be the amount received by the Company therefor, before deduction of
reasonable commissions, underwriting discounts or allowances or other reasonable
expenses paid or incurred by the Company in connection with such issuance, grant
or sale. In case any Common Stock, Options or Convertible Securities are issued
or sold for a consideration part or all of which shall be other than cash, the
amount of the consideration other than cash received by the Company will be the
fair value of such consideration, except where such consideration consists of
securities, in which case the amount of consideration received by the Company
will be the Market Price thereof as of the date of receipt. The fair value of
any consideration other than cash or securities will be determined in good faith
by the Board of Directors of the Company.

                                    (vi) EXCEPTIONS TO ADJUSTMENT OF EXERCISE
PRICE. No adjustment to the Exercise Price will be made (i) upon the exercise of
any warrants, options or convertible securities granted, issued and outstanding
on the date of issuance of this Warrant; (ii) upon the grant or exercise of any
stock or options which may hereafter be granted or exercised under any employee
benefit plan of the Company now existing or to be implemented in the future, so
long as the issuance of such stock or options is approved by a majority of the
independent members of the Board of Directors of the Company or a majority of
the members of



                                      -5-
<PAGE>   6

a committee of independent directors established for such purpose; or (iii) upon
the exercise of the Warrants.

                           (c) SUBDIVISION OR COMBINATION OF COMMON STOCK. If
the Company at any time subdivides (by any stock split, stock dividend,
recapitalization, reorganization, reclassification or otherwise) the shares of
Common Stock acquirable hereunder into a greater number of shares, then, after
the date of record for effecting such subdivision, the Exercise Price in effect
immediately prior to such subdivision will be proportionately reduced. If the
Company at any time combines (by reverse stock split, recapitalization,
reorganization, reclassification or otherwise) the shares of Common Stock
acquirable hereunder into a smaller number of shares, then, after the date of
record for effecting such combination, the Exercise Price in effect immediately
prior to such combination will be proportionately increased.

                           (d) ADJUSTMENT IN NUMBER OF SHARES. Upon each
adjustment of the Exercise Price pursuant to the provisions of this Paragraph 4,
the number of shares of Common Stock issuable upon exercise of this Warrant
shall be adjusted by multiplying a number equal to the Exercise Price in effect
immediately prior to such adjustment by the number of shares of Common Stock
issuable upon exercise of this Warrant immediately prior to such adjustment and
dividing the product so obtained by the adjusted Exercise Price.

                           (e) CONSOLIDATION, MERGER OR SALE. In case of any
consolidation of the Company with, or merger of the Company into any other
corporation, or in case of any sale or conveyance of all or substantially all of
the assets of the Company other than in connection with a plan of complete
liquidation of the Company, then:

                                    (1) If the fair value per share of Common
Stock of the shares of stock, securities or assets that are to be issued or paid
to the Company or its common shareholders in such consolidation, merger, sale or
conveyance, is greater than the then applicable Exercise Price, the Company
shall have the right to declare this Warrant to be exercised in full (using the
Cashless Exercise described herein), effective as of a date immediately prior to
the closing of such consolidation, merger, sale or conveyance. The Company shall
provide notice of its intent to make such a declaration (which intent may be
subject to fluctuations in the fair value of the consideration to be received in
such consolidation, merger, sale or conveyance) a reasonable time prior to the
anticipated closing of the consolidation, merger, sale or conveyance, and in no
case less than 10 business days prior to such closing. The declaration shall be
made in writing and provided to the holder of this Warrant on or as soon as
reasonably practicable after the effective date of such declaration. Upon such
declaration this Warrant shall be deemed to represent only the right to receive
such shares of stock, securities or assets as may be issued or paid with respect
to or in exchange for the number of shares of Common Stock acquirable and
receivable upon the Cashless Exercise of this Warrant on the effective date of
such declaration. The exercise of this Warrant pursuant to the Company's
declaration as just described shall be void and of no effect if the
consolidation, merger, sale or conveyance giving rise to the declaration does
not close within 10 business days after the effective date of such declaration.



                                      -6-
<PAGE>   7

Or, if the Company does not or cannot declare this Warrant to be exercised in
full,

                                    (2) As a condition of such consolidation,
merger or sale or conveyance, adequate provision will be made whereby the holder
of this Warrant will have the right to acquire and receive upon exercise of this
Warrant in lieu of the shares of Common Stock immediately theretofore acquirable
upon the exercise of this Warrant, such shares of stock, securities or assets as
may be issued or payable with respect to or in exchange for the number of shares
of Common Stock immediately theretofore acquirable and receivable upon exercise
of this Warrant had such consolidation, merger or sale or conveyance not taken
place. In any such case, the Company will make appropriate provision to insure
that the provisions of this Paragraph 4 hereof will thereafter be applicable as
nearly as may be in relation to any shares of stock or securities thereafter
deliverable upon the exercise of this Warrant.

                  The Company will not effect any consolidation, merger or sale
or conveyance unless the Company declares the exercise in full of this Warrant
or, prior to the consummation of such consolidation, merger, sale or conveyance,
the successor or acquiring entity (if other than the Company) and, if an entity
different from the successor or acquiring entity, the entity whose capital stock
or assets the holders of the Common Stock of the Company are entitled to receive
as a result of such consolidation, merger or sale or conveyance assumes by
written instrument the obligations under this Warrant (including under this
Paragraph 4) and the obligations to deliver to the holder of this Warrant such
shares of stock, securities or assets as, in accordance with the foregoing
provisions, the holder may be entitled to acquire.

                           (f) DISTRIBUTION OF ASSETS. In case the Company shall
declare or make any distribution of its assets (including cash) to holders of
Common Stock as a partial liquidating dividend, by way of return of capital or
otherwise, then, after the date of record for determining stockholders entitled
to such distribution, but prior to the date of distribution, the holder of this
Warrant shall be entitled upon exercise of this Warrant for the purchase of any
or all of the shares of Common Stock subject hereto, to receive the amount of
such assets which would have been payable to the holder had such holder been the
holder of such shares of Common Stock on the record date for the determination
of stockholders entitled to such distribution.

                           (g) NOTICE OF ADJUSTMENT. Upon the occurrence of any
event which requires any adjustment of the Exercise Price, then, and in each
such case, the Company shall give notice thereof to the holder of this Warrant,
which notice shall state the Exercise Price resulting from such adjustment and
the increase or decrease in the number of Warrant Shares purchasable at such
price upon exercise, setting forth in reasonable detail the method of
calculation and the facts upon which such calculation is based. Such calculation
shall be certified by the chief financial officer of the Company.

                           (h) MINIMUM ADJUSTMENT OF EXERCISE PRICE. No
adjustment of the Exercise Price shall be made in an amount of less than 1% of
the Exercise Price in effect at the time such adjustment is otherwise required
to be made, but any such lesser adjustment shall be


                                      -7-
<PAGE>   8
carried forward and shall be made at the time and together with the next
subsequent adjustment which, together with any adjustments so carried forward,
shall amount to not less than 1% of such Exercise Price.

                           (i) NO FRACTIONAL SHARES. No fractional shares of
Common Stock are to be issued upon the exercise of this Warrant, but the Company
shall pay a cash adjustment in respect of any fractional share which would
otherwise be issuable in an amount equal to the same fraction of the Market
Price of a share of Common Stock on the date of such exercise.

                           (j) OTHER NOTICES. In case at any time:

                                    (i) the Company shall declare any dividend
upon the Common Stock payable in shares of stock of any class or make any other
distribution (including dividends or distributions payable in cash out of
retained earnings) to the holders of the Common Stock;

                                    (ii) the Company shall offer for
subscription pro rata to the holders of the Common Stock any additional shares
of stock of any class or other rights;

                                    (iii) there shall be any capital
reorganization of the Company, or reclassification of the Common Stock, or
consolidation or merger of the Company with or into, or sale of all or
substantially all its assets to, another corporation or entity; or

                                    (iv) there shall be a voluntary or
involuntary dissolution, liquidation or winding-up of the Company;

then, in each such case, the Company shall give to the holder of this Warrant
(a) notice of the date on which the books of the Company shall close or a record
shall be taken for determining the holders of Common Stock entitled to receive
any such dividend, distribution, or subscription rights or for determining the
holders of Common Stock entitled to vote in respect of any such reorganization,
reclassification, consolidation, merger, sale, dissolution, liquidation or
winding-up and (b) in the case of any such reorganization, reclassification,
consolidation, merger, sale, dissolution, liquidation or winding-up, notice of
the date (or, if not then known, a reasonable approximation thereof by the
Company) when the same shall take place. Such notice shall also specify the date
on which the holders of Common Stock shall be entitled to receive such dividend,
distribution, or subscription rights or to exchange their Common Stock for stock
or other securities or property deliverable upon such reorganization,
reclassification, consolidation, merger, sale, dissolution, liquidation, or
winding-up, as the case may be. Such notice shall be given at least 30 days
prior to the record date or the date on which the Company's books are closed in
respect thereto. Failure to give any such notice or any defect therein shall not
affect the validity of the proceedings referred to in clauses (i), (ii), (iii)
and (iv) above.

                           (k) CERTAIN EVENTS. If any event occurs of the type
contemplated by the adjustment provisions of this Paragraph 4 but not expressly
provided for by such provisions, the Company will give notice of such event as
provided in Paragraph 4(g) hereof, and the



                                      -8-
<PAGE>   9

Company's Board of Directors will make an appropriate adjustment in the Exercise
Price and the number of shares of Common Stock acquirable upon exercise of this
Warrant so that the rights of the Holder shall be neither enhanced nor
diminished by such event.

                           (l) CERTAIN DEFINITIONS.

                                    (i) "COMMON STOCK DEEMED OUTSTANDING" shall
mean the number of shares of Common Stock actually outstanding (not including
shares of Common Stock held in the treasury of the Company), plus (x) pursuant
to Paragraph 4(b)(i) hereof, the maximum total number of shares of Common Stock
issuable upon the exercise of Options, as of the date of such issuance or grant
of such Options, if any, and (y) pursuant to Paragraph 4(b)(ii) hereof, the
maximum total number of shares of Common Stock issuable upon conversion or
exchange of Convertible Securities, as of the date of issuance of such
Convertible Securities, if any.

                                    (ii) "MARKET PRICE," as of any date, (i)
means the average of the last reported sale prices for the shares of Common
Stock on the Nasdaq National Market (the "NNM") for the five (5) trading days
immediately preceding such date as reported by Bloomberg Financial Markets or an
equivalent reliable reporting service mutually acceptable to and hereafter
designated by the holder of this Warrant and the Company ("Bloomberg"), or (ii)
if the NNM is not the principal trading market for the shares of Common Stock,
the average of the last reported sale prices on the principal trading market for
the Common Stock during the same period as reported by Bloomberg, or (iii) if
market value cannot be calculated as of such date on any of the foregoing bases,
the Market Price shall be the fair market value as reasonably determined in good
faith by (a) the Board of Directors of the Corporation or (b) at the option of a
majority-in-interest of the holders of the outstanding Warrants, by an
independent investment bank of nationally recognized standing in the valuation
of businesses similar to the business of the corporation. The manner of
determining the Market Price of the Common Stock set forth in the foregoing
definition shall apply with respect to any other security in respect of which a
determination as to market value must be made hereunder.

                                    (iii) "COMMON STOCK," for purposes of this
Paragraph 4, includes the Common Stock, par value $0.01 per share, and any
additional class of stock of the Company having no preference as to dividends or
distributions on liquidation, provided that the shares purchasable pursuant to
this Warrant shall include only shares of Common Stock, par value $0.01 per
share, in respect of which this Warrant is exercisable, or shares resulting from
any subdivision or combination of such Common Stock, or in the case of any
reorganization, reclassification, consolidation, merger, or sale of the
character referred to in Paragraph 4(e) hereof, the stock or other securities or
property provided for in such Paragraph.

                  5. ISSUE TAX. The issuance of certificates for Warrant Shares
upon the exercise of this Warrant shall be made without charge to the holder of
this Warrant or such shares for any issuance tax or other costs in respect
thereof, provided that the Company shall not be required to pay any tax which
may be payable in respect of any transfer involved in the issuance and delivery
of any certificate in a name other than the holder of this Warrant.



                                      -9-
<PAGE>   10

                  6. NO RIGHTS OR LIABILITIES AS A SHAREHOLDER. This Warrant
shall not entitle the holder hereof to any voting rights or other rights as a
shareholder of the Company. No provision of this Warrant, in the absence of
affirmative action by the holder hereof to purchase Warrant Shares, and no mere
enumeration herein of the rights or privileges of the holder hereof, shall give
rise to any liability of such holder for the Exercise Price or as a shareholder
of the Company, whether such liability is asserted by the Company or by
creditors of the Company.

                  7. TRANSFER, EXCHANGE, AND REPLACEMENT OF WARRANT.

                           (a) RESTRICTION ON TRANSFER. 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 assignment in the
form attached hereto, at the office or agency of the Company referred to in
Paragraph 7(e) below, provided, however, that any transfer or assignment shall
be subject to the conditions set forth in Paragraph 7(f) hereof and to all
applicable securities laws. Until due presentment for registration of transfer
on the books of the Company, the Company may treat the registered holder hereof
as the owner and holder hereof for all purposes, and the Company shall not be
affected by any notice to the contrary.

                           (b) WARRANT EXCHANGEABLE FOR DIFFERENT DENOMINATIONS.
This Warrant is exchangeable, upon the surrender hereof by the holder hereof at
the office or agency of the Company referred to in Paragraph 7(e) below, for new
Warrants of like tenor representing in the aggregate the right to purchase the
number of shares of Common Stock which may be purchased hereunder, each of such
new Warrants to represent the right to purchase such number of shares as shall
be designated by the holder hereof at the time of such surrender.

                           (c) REPLACEMENT OF WARRANT. Upon receipt of evidence
reasonably satisfactory to the Company of the loss, theft, destruction, or
mutilation of this Warrant and, in the case of any such loss, theft, or
destruction, upon delivery of an indemnity agreement reasonably satisfactory in
form and amount to the Company, or, in the case of any such mutilation, upon
surrender and cancellation of this Warrant, the Company, at its expense, will
execute and deliver, in lieu thereof, a new Warrant of like tenor.

                           (d) CANCELLATION; PAYMENT OF EXPENSES. Upon the
surrender of this Warrant in connection with any transfer, exchange, or
replacement as provided in this Paragraph 7, this Warrant shall be promptly
canceled by the Company. The Company shall pay all taxes (other than securities
transfer taxes) and all other expenses (other than legal expenses, if any,
incurred by the Holder or transferees) and charges payable in connection with
the preparation, execution, and delivery of Warrants pursuant to this Paragraph
7.

                           (e) REGISTER. 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
and each prior owner of this Warrant.



                                      -10-
<PAGE>   11

                           (f) EXERCISE OR TRANSFER WITHOUT REGISTRATION. If, at
the time of the surrender of this Warrant in connection with any exercise,
transfer, or exchange of this Warrant, this Warrant (or, in the case of any
exercise, the Warrant Shares issuable hereunder), shall not be registered under
the Securities Act and under applicable state securities or blue sky laws, the
Company may require, as a condition of allowing such exercise, transfer, or
exchange, (i) that the holder or transferee of this Warrant, as the case may be,
furnish to the Company a written opinion of counsel, which opinion and counsel
are acceptable to the Company, to the effect that such exercise, transfer, or
exchange may be made without registration under said Act and under applicable
state securities or blue sky laws, (ii) that the holder or transferee execute
and deliver to the Company an investment letter in form and substance acceptable
to the Company and (iii) that the transferee be an "accredited investor" as
defined in Rule 501(a) promulgated under the Securities Act; provided that no
such opinion, letter or status as an "accredited investor" shall be required in
connection with a transfer pursuant to Rule 144 under the Securities Act. The
first holder of this Warrant, by taking and holding the same, represents to the
Company that such holder is acquiring this Warrant for investment and not with a
view to the distribution thereof.

                  8. REGISTRATION RIGHTS. The initial holder of this Warrant is
entitled to the benefit of such registration rights in respect of the Warrant
Shares as are set forth in Section 2 of that certain Registration Rights
Agreement by and between the Company and RGC International Investors, LDC, to be
dated April 17, 2000.

                  9. NOTICES. All notices, requests, and other communications
required or permitted to be given or delivered hereunder to the holder of this
Warrant shall be in writing, and shall be personally delivered, or shall be sent
by certified or registered mail or by recognized overnight mail courier, postage
prepaid and addressed, to such holder at the address shown for such holder on
the books of the Company, or at such other address as shall have been furnished
to the Company by notice from such holder. All notices, requests, and other
communications required or permitted to be given or delivered hereunder to the
Company shall be in writing, and shall be personally delivered, or shall be sent
by certified or registered mail or by recognized overnight mail courier, postage
prepaid and addressed, to the office of the Company at 67 Inverness Drive East,
Suite 100, Englewood, Colorado 80112, Attention: Chief Executive Officer, or at
such other address as shall have been furnished to the holder of this Warrant by
notice from the Company. Any such notice, request, or other communication may be
sent by facsimile, but shall in such case be subsequently confirmed by a writing
personally delivered or sent by certified or registered mail or by recognized
overnight mail courier as provided above. All notices, requests, and other
communications shall be deemed to have been given either at the time of the
receipt thereof by the person entitled to receive such notice at the address of
such person for purposes of this Paragraph 9, or, if mailed by registered or
certified mail or with a recognized overnight mail courier upon deposit with the
United States Post Office or such overnight mail courier, if postage is prepaid
and the mailing is properly addressed, as the case may be.

                  10. GOVERNING LAW. THIS WARRANT SHALL BE GOVERNED BY AND
CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF COLORADO



                                      -11-
<PAGE>   12

APPLICABLE TO AGREEMENTS MADE AND TO BE PERFORMED IN THE STATE OF COLORADO
(WITHOUT REGARD TO PRINCIPLES OF CONFLICT OF LAWS). BOTH PARTIES IRREVOCABLY
CONSENT TO THE EXCLUSIVE JURISDICTION OF THE UNITED STATES FEDERAL COURTS AND
THE STATE COURTS LOCATED IN COLORADO WITH RESPECT TO ANY SUIT OR PROCEEDING
BASED ON OR ARISING UNDER THIS AGREEMENT, THE AGREEMENTS ENTERED INTO IN
CONNECTION HEREWITH OR THE TRANSACTIONS CONTEMPLATED HEREBY OR THEREBY AND
IRREVOCABLY AGREE THAT ALL CLAIMS IN RESPECT OF SUCH SUIT OR PROCEEDING MAY BE
DETERMINED IN SUCH COURTS. BOTH PARTIES IRREVOCABLY WAIVE THE DEFENSE OF AN
INCONVENIENT FORUM TO THE MAINTENANCE OF SUCH SUIT OR PROCEEDING. BOTH PARTIES
FURTHER AGREE THAT SERVICE OF PROCESS UPON A PARTY MAILED BY FIRST CLASS MAIL
SHALL BE DEEMED IN EVERY RESPECT EFFECTIVE SERVICE OF PROCESS UPON THE PARTY IN
ANY SUCH SUIT OR PROCEEDING. NOTHING HEREIN SHALL AFFECT EITHER PARTY'S RIGHT TO
SERVE PROCESS IN ANY OTHER MANNER PERMITTED BY LAW. BOTH PARTIES AGREE THAT A
FINAL NON-APPEALABLE JUDGMENT IN ANY SUCH SUIT OR PROCEEDING SHALL BE CONCLUSIVE
AND MAY BE ENFORCED IN OTHER JURISDICTIONS BY SUIT ON SUCH JUDGMENT OR IN ANY
OTHER LAWFUL MANNER.

                  11. MISCELLANEOUS.

                           (a) AMENDMENTS. This Warrant and any provision hereof
may only be amended by an instrument in writing signed by the Company and the
holder hereof.

                           (b) DESCRIPTIVE HEADINGS. The descriptive headings of
the several paragraphs of this Warrant are inserted for purposes of reference
only, and shall not affect the meaning or construction of any of the provisions
hereof.

                           (c) CASHLESS EXERCISE. Notwithstanding anything to
the contrary contained in this Warrant, if the resale of the Warrant Shares by
the holder is not then registered pursuant to an effective registration
statement under the Securities Act, this Warrant may be exercised 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"). In the event of a Cashless Exercise, in lieu of paying the
Exercise Price in cash, the holder shall surrender this Warrant for that number
of shares of Common Stock determined by multiplying the number of Warrant Shares
to which it would otherwise be entitled by a fraction, the numerator of which
shall be the difference between the then current Market Price per share of the
Common Stock and the Exercise Price, and the denominator of which shall be the
then current Market Price per share of Common Stock.

                           (d) REMEDIES. The Company acknowledges that a breach
by it of its obligations hereunder will cause irreparable harm to the holder, by
vitiating the intent and



                                      -12-
<PAGE>   13

purpose of the transaction contemplated hereby. Accordingly, the Company
acknowledges that the remedy at law for a breach of its obligations under this
Warrant will be inadequate and agrees, in the event of a breach or threatened
breach by the Company of the provisions of this Warrant, that the holder shall
be entitled, in addition to all other available remedies at law or in equity, to
an injunction or injunctions restraining, preventing or curing any breach of
this Warrant and to enforce specifically the terms and provisions thereof,
without the necessity of showing economic loss and without any bond or other
security being required.


                  IN WITNESS WHEREOF, the Company has caused this Warrant to be
signed by its duly authorized officer.

                                       T-NETIX, INC.


                                       By:
                                          --------------------------------------
                                          Alvyn A. Schopp
                                          Chief Executive Officer


Dated as of April 14, 2000



                                      -13-
<PAGE>   14

                           FORM OF EXERCISE AGREEMENT


                                       Dated:  ________ __, 200_


To: T-NETIX, Inc.


                  The undersigned, pursuant to the provisions set forth in the
within Warrant, hereby agrees to purchase ________ shares of Common Stock
covered by such Warrant, and makes payment herewith in full therefor at the
price per share provided by such Warrant in cash or by certified or official
bank check in the amount of, or, if the resale of such Common Stock by the
undersigned is not currently registered pursuant to an effective registration
statement under the Securities Act of 1933, as amended, by surrender of
securities issued by the Company (including a portion of the Warrant) having a
market value (in the case of a portion of this Warrant, determined in accordance
with Section 11(c) of the Warrant) equal to $_________. Please issue a
certificate or certificates for such shares of Common Stock in the name of and
pay any cash for any fractional share to:


Name:
               -----------------------------

Signature:
               -----------------------------

Address:
               -----------------------------

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


                                       Note: The above signature should
                                       correspond exactly with the name on the
                                       face of the within Warrant.

and, if said number of shares of Common Stock shall not be all the shares
purchasable under the within Warrant, a new Warrant is to be issued in the name
of said undersigned covering the balance of the shares purchasable thereunder
less any fraction of a share paid in cash.



<PAGE>   15

                               FORM OF ASSIGNMENT


                  FOR VALUE RECEIVED, the undersigned hereby sells, assigns, and
transfers all the rights of the undersigned under the within Warrant, with
respect to the number of shares of Common Stock covered thereby set forth
hereinbelow, to:

Name of Assignee                        Address                     No of Shares






, and hereby irrevocably constitutes and appoints ______________________________
as agent and attorney-in-fact to transfer said Warrant on the books of the
within-named corporation, with full power of substitution in the premises.


Dated:  _____________, 200__

In the presence of:


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


Name:
     ---------------------------------------

Signature:
          ----------------------------------

Title of Signing Officer or Agent (if any):

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

Address:
        ------------------------------------

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


                                       Note: The above signature should
                                       correspond exactly with the name on the
                                       face of the within Warrant.