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                                                                   Exhibit 4(b)

                            UGLY DUCKLING CORPORATION

                                WARRANT AGREEMENT

         THIS WARRANT AGREEMENT (the "Agreement"), dated as of February 12,
1998, is between UGLY DUCKLING CORPORATION, a Delaware corporation (the
"Company"), and each of the Lenders (as defined below).

         WHEREAS, the Company has entered into a Loan Agreement dated as of
February 12, 1998 (the "Loan Agreement"), by and among the Company and the
lenders named therein (the "Lenders"), pursuant to which the Lenders will make
term loans to the Company, all as set forth in, and subject to the terms and
conditions of, the Loan Agreement; and

         WHEREAS, as a condition precedent to the execution and delivery of the
Loan Agreement, the Company has agreed to issue to the Lenders warrants (the
"Warrants") to purchase shares of common stock, $.001 par value per share
("Common Stock"), of the Company, subject to the terms and conditions of this
Agreement.

         NOW, THEREFORE, in consideration of the promises and the mutual
agreements herein set forth, the parties agree as follows:

         Section 1.        ISSUANCE OF WARRANTS AND FORM OF WARRANTS.

         (a) Subject to the terms and conditions hereof, the Company shall issue
to the Lenders and the Lenders shall accept from the Company, 500,000 Warrants
substantially in the form of Exhibit A hereto. Each Lender shall be issued the
number of Warrants set forth beside such Lender's name on Exhibit B hereto.

         (b) Each Warrant shall entitle the registered holder of the certificate
representing such Warrant to purchase upon the exercise thereof one share of
Common Stock, subject to the adjustments provided for in Section 8 hereof, at
any time until the later of (i) 1:30 p.m., Phoenix, Arizona time, on February
12, 2001 or (ii) such time as the Notes issued pursuant to the Loan Agreement
have been paid in full, unless earlier redeemed pursuant to Section 10 hereof.

         (c) The Warrant certificates shall be in registered form only. Each
Warrant certificate shall be dated as of the date of issuance thereof (whether
upon initial issuance or upon transfer or exchange), and shall be executed on
behalf of the Company by the manual signature of its President or a Vice
President, and attested to by the manual signature of its Secretary or an
Assistant Secretary. In case any officer of the Company who shall have signed
any Warrant certificate shall cease to be such officer of the Company prior to
the issuance thereof, such Warrant certificate may nevertheless be issued and
delivered with the same force and effect as though the person who signed the
same had not ceased to be such officer of the Company.

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         Section 2. EXERCISE OF WARRANTS, DURATION AND WARRANT PRICE. Subject to
the provisions of this Agreement, each registered holder of one or more Warrant
certificates shall have the right, which may be exercised as provided in such
Warrant certificates, to purchase from the Company (and the Company shall issue
and sell to such registered holder) the number of shares of Common Stock or
other securities to which the Warrants represented by such certificates are at
the time entitled hereunder.

         (a) Each Warrant not exercised by its expiration date shall become
void, and all rights thereunder and all rights in respect thereof under this
Agreement shall cease on such date.

         (b) A Warrant may be exercised by the surrender of the certificate
representing such Warrant to the Company with the subscription form set forth on
the reverse thereof duly executed and properly endorsed with the signatures
properly guaranteed, and upon payment in full to the Company of the Warrant
Price (as hereinafter defined) for the number of shares of Common Stock or other
securities as to which the Warrant is exercised. Such Warrant Price shall be
paid in full in cash, or by certified check or bank draft payable in United
States currency to the order of the Company or by surrender of this Warrant to
the Company together with a notice of cashless exercise, in which event the
Company shall issue to the registered holder the number of shares of Common
Stock determined as follows:

                           X = Y x (A-B)/A

                           X = the number of shares of Common Stock to be issued
                           to the registered holder.

                           Y = the number of shares of Common Stock with respect
                           to which the Warrant is being exercised.

                           A = the Current Market Price determined as of the
                           date of exercise.

                           B = the Warrant Price.

         (c) Subject to adjustment in accordance with Section 8 hereof, the
price per share of Common Stock at which each Warrant may be exercised (the
"Warrant Price") shall be Ten Dollars ($10.00).

         (d) Subject to the further provisions of this Section 2 and of Section
5 hereof, upon surrender of Warrant certificates and payment of the Warrant
Price, the Company shall issue and cause to be delivered, as promptly as
practicable to or upon the written order of the registered holder of such
Warrants and in such name or names as such registered holder may designate,
subject to applicable securities laws, a certificate or certificates for the
number of securities so purchased upon the exercise of such Warrants, together
with cash, as provided in Section 9 of this Agreement, in respect of any
fraction of a share or security otherwise issuable upon such surrender. All
shares of


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Common Stock or other such securities issued upon the exercise of a Warrant
shall be duly authorized, validly issued, fully paid and nonassessable and free
and clear of all liens and other encumbrances.

         (e) Certificates representing such securities shall be deemed to have
been issued and any person so designated to be named therein shall be deemed to
have become a holder of record of such securities as of the date of the
surrender of such Warrants and payment of the Warrant Price. The rights of
purchase represented by each Warrant certificate shall be exercisable, at the
election of the registered holder thereof, either as an entirety or from time to
time for part of the number of securities specified therein and, in the event
that any Warrant certificate is exercised in respect of less than all of the
securities specified therein at any time prior to the expiration date of the
Warrant certificate, a new Warrant certificate or certificates will be issued to
such registered holder for the remaining number of securities specified in the
Warrant certificate so surrendered.

         Section 3.        COUNTERSIGNATURE AND REGISTRATION.

         (a) The Company shall maintain books (the "Warrant Register") for the
registration and the registration of transfer of the Warrants. Upon the initial
issuance of the Warrants, the Company shall issue and register the Warrants in
the names of the Lenders in accordance with Section 1 hereof.

         (b) Prior to due presentment for registration of transfer of any
Warrant certificate, the Company may deem and treat the person in whose name
such Warrant certificate shall be registered upon the Warrant Register (the
"registered holder") as the absolute owner of such Warrant certificate and of
each Warrant represented thereby (notwithstanding any notation of ownership or
other writing on the Warrant certificate made by anyone other than the Company),
for the purpose of any exercise thereof, of any distribution or notice to the
holder thereof, and for all other purposes, and the Company shall not be
affected by any notice to the contrary.

         Section 4.        TRANSFER AND EXCHANGE OF WARRANTS.

         (a) The Company shall register the transfer, from time to time, of any
outstanding Warrant or portion thereof upon the Warrant Register, upon surrender
of the certificate evidencing such Warrant for transfer, properly endorsed with
signatures properly guaranteed and accompanied by appropriate instructions for
transfer. Upon any such transfer, a new Warrant certificate representing an
equal aggregate number of Warrants so transferred shall be issued to the
transferee and the surrendered Warrant certificate shall be canceled by the
Company. In the event that only a portion of a Warrant is transferred at any
time, a new Warrant certificate representing the remaining portion of the
Warrant will also be issued to the transferring holder. Notwithstanding anything
to the contrary herein, no transfer or exchange may be made except in compliance
with applicable securities laws and Section 12 hereof.



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         (b) Warrant certificates may be surrendered to the Company, together
with a written request for exchange, and thereupon the Company shall issue in
exchange therefor one or more new Warrant certificates as requested by the
registered holder of the Warrant certificate or certificates so surrendered,
representing an equal aggregate number of Warrants.

         (c) The Company shall not be required to effect any registration of
transfer or exchange which will result in the issuance of a Warrant certificate
for a fraction of a Warrant.

         (d) No service charge shall be made for any exchange or registration of
transfer of Warrant certificates.

         Section 5. PAYMENT OF TAXES. The Company will pay any documentary stamp
taxes attributable to the initial issuance or delivery of the shares of Common
Stock or other securities issuable upon the exercise of Warrants; provided,
however, the Company shall not be required to pay any tax or taxes which may be
payable in respect of any transfer of the Warrants or involved in the issuance
or delivery of any Warrant certificate or certificates for shares of Common
Stock in a name other than registered holder of Warrants in respect of which
such shares are issued, and in such case the Company shall not be required to
issue or deliver any certificate for shares of Common Stock or any Warrant
certificate until the person requesting the same has paid to the Company the
amount of such tax or has established to the Company's satisfaction that such
tax has been paid.

         Section 6. MUTILATED OR MISSING WARRANTS. In case any of the Warrant
certificates shall be mutilated, lost, stolen or destroyed, the Company may
issue and deliver in exchange and substitution for and upon cancellation of the
mutilated Warrant certificate, or in lieu of and substitution for the Warrant
certificate lost, stolen or destroyed, a new Warrant certificate representing an
equal aggregate number of Warrants, but only upon receipt of evidence
satisfactory to the Company of such loss, theft or destruction of such Warrant
certificate and reasonable indemnity, if requested, also satisfactory to it.
Applicants for such substitute Warrant certificates shall also comply with such
other reasonable conditions and pay such reasonable charges as the Company may
prescribe.

         Section 7.        RESERVATION OF COMMON STOCK.

         (a) There have been reserved, and the Company shall at all times keep
reserved, out of its authorized and unissued shares of Common Stock, a number of
shares sufficient to provide for the exercise of the rights of purchase
represented by the Warrants then outstanding or issuable upon exercise, and the
transfer agent for the Common Stock and every subsequent transfer agent for any
shares of the Company's capital stock issuable upon the exercise of any of the
rights of purchase aforesaid are hereby irrevocably authorized and directed at
all times to reserve such number of authorized and unissued shares as shall be
requisite for such purpose. The Company will keep a copy of this Agreement on
file with the transfer agent for the Common Stock and with every subsequent
transfer agent for any shares of the Company's capital stock issuable upon the
exercise of the rights of purchase represented by the Warrants.


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         (b) The Company will supply such transfer agent with duly executed
certificates and will provide or otherwise make available any cash as provided
in Section 9 of this Agreement. All Warrant certificates surrendered in the
exercise thereby evidenced shall be canceled by the Company. After the
expiration date of the Warrants, no shares of Common Stock shall be subject to
reservation in respect of such Warrants.

         Section 8. ADJUSTMENT OF WARRANT PRICE AND NUMBER OF SHARES OF COMMON
STOCK. The number and kind of securities purchasable upon the exercise of the
Warrants and the Warrant Price shall be subject to adjustment from time to time
upon the happening of certain events, as follows:

         8.1 ADJUSTMENTS. The number of shares of Common Stock or other
securities purchasable upon the exercise of each Warrant and the Warrant Price
shall be subject to adjustment as follows:

                  (a) If the Company (i) pays a dividend in Common Stock or
makes a distribution in Common Stock or shares convertible in Common Stock, (ii)
subdivides its outstanding Common Stock into a greater number of shares, (iii)
combines its outstanding Common Stock into a smaller number of shares, or (iv)
issues, by reclassification of its Common Stock, other securities of the
Company, then the number and kind of shares of Common Stock or other securities
purchasable upon exercise of a Warrant immediately prior thereto will be
adjusted so that the holder of a Warrant will be entitled to receive the kind
and number of shares of Common Stock or other securities of the Company that
such holder would have owned and would have been entitled to receive immediately
after the happening of any of the events described above, had the Warrant been
exercised immediately prior to the happening of such event or any record date
with respect thereto. Any adjustment made pursuant to this subsection 8.1(a)
will become effective immediately after the effective date of such event
retroactive to the record date, if any, for such event.

                  (b) If the Company issues or sell any shares of Common Stock
or any rights or warrants to purchase shares of Common Stock or securities
convertible into Common Stock at a price per share of Common Stock that is less
than 90% of the Daily Market Price (as defined in Section 10(e) hereof) of the
Common Stock as of the trading day immediately preceding (or the same day if
trading has been completed for such day) of such issuance or sale, the Warrant
Price shall be reduced by multiplying the Warrant Price in effect on the date of
issuance of such shares, warrants, rights or convertible securities by a
fraction, the denominator of which shall be the number of shares of Common Stock
(excluding treasury shares, if any) outstanding on the date of issuance of such
shares, rights, warrants or convertible securities plus the number of additional
shares of Common Stock offered for subscription or purchase or issuable on
conversion, and the numerator of which shall be the number of shares of Common
Stock (excluding treasury shares, if any) outstanding on the date of issuance of
such shares, rights, warrants or convertible securities plus the number of
shares which the aggregate offering price of the total number of shares so
offered, issued or issuable, or, with respect to convertible securities, the
aggregate consideration received or to be received by the Company for the
convertible securities, would purchase at such Daily Market Price. Such


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adjustment shall be made successively whenever such shares, rights, warrants or
convertible securities are issued and shall become effective immediately after
the date of such issuance. However, upon the expiration of any right or warrant
to purchase Common Stock or conversion right, the issuance of which resulted in
an adjustment in the Warrant Price, if any such right, warrant or conversion
right shall expire and shall not have been exercised, the Warrant Price shall
immediately upon such expiration be recomputed and effective immediately upon
such expiration be increased to the price which it would have been (but
reflecting any other adjustments in the Warrant Price made pursuant to the
provisions of this Section 8.1(b) after the issuance of such rights, warrants or
convertible securities) had the adjustment of the Warrant Price upon the
issuance of such rights, warrants or convertible securities been made on the
basis of offering for subscription or purchase only that number of shares of
Common Stock actually purchased upon the exercise of such rights or warrants
actually exercised or the conversion of the convertible securities actually
converted.

                  (c) If the Company distributes to all holders of Common Stock
evidences of its indebtedness or assets (excluding cash dividends or cash
distributions paid out of earned surplus and made in the ordinary course of
business) or rights to subscribe for or purchase any security, then in each such
case the Warrant Price shall be determined by multiplying the Warrant Price in
effect prior to the record date fixed for determination of stockholders entitled
to receive such distribution by a fraction, the denominator of which shall be
the Daily Market Price of Common Stock determined as of the record date
mentioned above, and the numerator of which shall be such Daily Market Price of
the Common Stock, less the then fair market value (as determined by the Board of
Directors of the Company in good faith, whose determination shall be conclusive
if made in good faith; provided, however, that in the event of a distribution or
series of related distributions exceeding 10% of the net assets of the Company,
then such fair market value shall be determined by a nationally recognized or
major regional investment banking firm or firm of independent certified public
accountants of recognized standing (which may be the firm that regularly
examines the financial statements of the Company) selected in good faith by the
Board of Directors of the Company, and in either case shall be described in a
statement provided to Warrant holders) of the portion of assets or evidences of
indebtedness so distributed or such subscription rights applicable to one share
of Common Stock. Such adjustment shall be made successively whenever any such
distribution is made and shall become effective immediately after the record
date mentioned above. In the event such distribution is not made, the Warrant
Price shall again be adjusted to the number that was in effect immediately prior
to such record date.

                  (d) No adjustment in the number of shares or securities
purchasable pursuant to the Warrants shall be required unless such adjustment
would require an increase or decrease of at least one percent in the number of
shares or securities then purchasable upon the exercise of the Warrants,
provided, however, that any adjustment which by reason of this subsection 8.1(d)
is not required to be made shall be carried forward and taken into account in
any subsequent adjustments.



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                  (e) The Company may, at its option, at any time during the
term of the Warrant, reduce the then current Warrant Price to any amount,
consistent with applicable law, deemed appropriate by the Board of Directors of
the Company.

                  (f) Whenever the number of shares or securities purchasable
upon the exercise of the Warrants is adjusted, as herein provided, the Warrant
Price for shares payable upon exercise of the Warrants shall be adjusted by
multiplying such Warrant Price immediately prior to such adjustment by a
fraction, the numerator of which shall be the number of shares purchasable upon
the exercise of the Warrant immediately prior to such adjustment, and the
denominator of which shall be the number of shares so purchasable immediately
thereafter.

                  (g) Whenever the number of shares or securities purchasable
upon the exercise of the Warrants and/or the Warrant Price is adjusted as herein
provided, the Company shall cause to be promptly mailed to each registered
holder of a Warrant by first class mail, postage prepaid, notice of such
adjustment and a certificate of the chief financial officer of the Company
setting forth the number of shares or securities purchasable upon the exercise
of the Warrants after such adjustment, the Warrant Price as adjusted, a brief
statement of the facts requiring such adjustment and the computation by which
such adjustment was made.

                  (h) For the purpose of this subsection 8.1, the term "Common
Stock" shall mean (i) the class of stock designated as the voting Common Stock
of the Company at the date of this Agreement, or (ii) any other class of stock
or securities resulting from successive changes or reclassifications of such
Common Stock consisting solely of changes in par value, or from par value to no
par value, or from no par value to par value. In the event that at any time, as
a result of an adjustment made pursuant to this Section 8, a registered holder
shall become entitled to purchase any securities of the Company other than
shares of Common Stock, thereafter the number of such other securities so
purchasable upon exercise of the Warrants shall be subject to adjustment from
time to time in a manner and on terms as nearly equivalent as practicable to the
provisions with respect to the shares contained in this Section 8.

         8.2 NO ADJUSTMENT FOR DIVIDENDS. Except as provided in subsection 8.1,
no adjustment in respect of any dividends or distributions shall be made during
the term of the Warrants or upon the exercise of the Warrants.

         8.3 NO ADJUSTMENT IN CERTAIN CASES. No adjustments are required to be
made pursuant to Section 8 hereof in connection with the issuance of shares of
Common Stock or the Warrants (or the underlying shares of Common Stock) in the
transactions contemplated by this Agreement.

         8.4 PRESERVATION OF PURCHASE RIGHTS UPON RECLASSIFICATION,
CONSOLIDATION, ETC. In case of any consolidation of the Company with or merger
of the Company into another corporation or in case of any sale or conveyance to
another corporation of the property, assets or business of the Company as an
entirety or substantially as an entirety, the Company or such successor or
purchasing corporation, as the case may be, shall execute an agreement with the
registered holders of the


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Warrants providing such holders with the right thereafter, upon payment of the
Warrant Price in effect immediately prior to such action, to purchase, upon
exercise of each Warrant, the kind and amount of shares and other securities and
property which it would have owned or have been entitled to receive after the
happening of such consolidation, merger, sale or conveyance had each Warrant
been exercised immediately prior to such action. Any such agreements referred to
in this subsection 8.4 shall provide for adjustments, which shall be as nearly
equivalent as may be practicable to the adjustments provided for in Section 8
hereof. The provisions of this subsection 8.4 shall similarly apply to
successive consolidations, mergers, sales, or conveyances.

         8.5 PAR VALUE OF SHARES OF COMMON STOCK. Before taking any action that
would cause an adjustment reducing the Warrant Price below the then par value of
the Common Stock issuable upon exercise of the Warrants, the Company will take
any corporate action which may, in the opinion of its counsel, be necessary in
order that the Company may validly and legally issue fully paid and
nonassessable Common Stock at such adjusted Warrant Price.

         8.6 INDEPENDENT PUBLIC ACCOUNTANTS. The Company may but shall not be
required to retain a firm of independent public accountants of recognized
regional or national standing (which may be any such firm regularly employed by
the Company) to make any computation required under this Section 8, and a
certificate signed by such firm shall be conclusive evidence of the correctness
of any computation made under this Section 8 and the Company shall cause to be
promptly mailed to each registered holder of a Warrant by first class mail,
postage prepaid, a copy of such certificate.

         8.7 STATEMENT ON WARRANT CERTIFICATES. Irrespective of any adjustments
in the Warrant Price or the number of securities issuable upon exercise of
Warrants, Warrant certificates theretofore or thereafter issued may continue to
express the same price and number of securities as are stated in the similar
Warrant certificates initially issuable pursuant to this Agreement. However, the
Company may, at any time in its sole discretion (which shall be conclusive),
make any change in the form of Warrant certificate that it may deem appropriate
and that does not affect the substance thereof; and any Warrant certificate
thereafter issued, whether upon registration of, transfer of, or in exchange or
substitution for, an outstanding Warrant certificate, may be in the form so
changed.

         8.8 NO RIGHTS AS STOCKHOLDER; NOTICES TO HOLDERS OF WARRANTS. If, at
any time prior to the expiration of a Warrant and prior to its exercise, any one
or more of the following events shall occur:

                  (a) any action that would require an adjustment pursuant to
subsection 8.1 or 8.4 hereof; or

                  (b) a dissolution, liquidation or winding up of the Company
(other than in connection with a consolidation, merger or sale of its property,
assets and business as an entirety or substantially as an entirety) shall be
proposed; then the Company must give notice in writing of such event to the
registered holders of the Warrants, as provided in Section 14 hereof, at least
20 days, to the extent practicable, prior to the date fixed as a record date or
the date of closing the transfer


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books for the determination of the stockholders entitled to any relevant
dividend, distribution, subscription rights or other rights or for the
determination of stockholders entitled to vote on such proposed dissolution,
liquidation or winding up. Such notice must specify such record date or the date
of closing the transfer books, as the case may be. Failure to mail or receive
such notice or any defect therein will not affect the validity of any action
taken with respect thereto.

         Section 9. FRACTIONAL INTERESTS. The Company is not required to issue
fractional shares of Common Stock on the exercise of a Warrant. If any fraction
of a share of Common Stock would, except for the provisions of this Section 9,
be issuable on the exercise of a Warrant (or specified portion thereof), the
Company will in lieu thereof pay an amount in cash equal to the then Current
Market Price multiplied by such fraction. For purposes of this Agreement, the
term "Current Market Price" means (i) if the Common Stock is listed for
quotation on the Nasdaq National Market or the Nasdaq SmallCap Market or on a
national securities exchange, the average for the 10 consecutive trading days
immediately preceding the date in question of the daily per share closing prices
of the Common Stock as quoted by the Nasdaq National Market or the Nasdaq
SmallCap Market or on the principal stock exchange on which it is listed, as the
case may be, whichever is the higher, or (ii) if the Common Stock is traded in
the over-the-counter market and is not listed for quotation on the Nasdaq
National Market or the Nasdaq SmallCap Market nor on any national securities
exchange, the average of the per share closing bid prices of the Common Stock on
the 10 consecutive trading days immediately preceding the date in question, as
reported by Nasdaq or an equivalent generally accepted reporting service. The
closing price referred to in clause (i) above shall be the last reported sale
price or, in case no such reported sale takes place on such day, the average of
the reported closing bid and asked prices, in either case as quoted by the
Nasdaq National Market or the Nasdaq SmallCap Market or on the national
securities exchange on which the Common Stock is then listed. For purposes of
clause (ii) above, if trading in the Common Stock is not reported by Nasdaq, the
bid price referred to in said clause shall be the lowest bid price as reported
on the OTC Bulletin Board or in the "pink sheets" published by National
Quotation Bureau, Incorporated.

         Section 10.       REDEMPTION.

         (a) The then outstanding Warrants may be redeemed, at the option of the
Company, at $.10 per share of Common Stock purchasable upon exercise of such
Warrants, at any time after the average Daily Market Price per share of the
Common Stock for a period of at least 20 consecutive trading days ending not
more than fifteen (15) days prior to the date of the notice given pursuant to
Section 10(b) hereof has equaled or exceeded $16.00, and prior to expiration of
the Warrants. The Daily Market Price of the Common Stock will be determined by
the Company in the manner set forth in Section 10(e) as of the end of each
trading day (or, if no trading in the Common Stock occurred on such day, as of
the end of the immediately preceding trading day in which trading occurred). All
outstanding Warrants must be redeemed if any are redeemed, and any right to
exercise an outstanding Warrant shall terminate at 1:30 p.m. (Phoenix, Arizona
time) on the date fixed for redemption. Trading day means a day in which trading
of securities occurred on the Nasdaq National Market.



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         (b) The Company may exercise its right to redeem the Warrants only by
giving the notice set forth in the following sentence. If the Company exercises
its right to redeem, it shall give notice to the registered holders of the
outstanding Warrants by mailing to such registered holders a notice of
redemption, first class, postage prepaid, at their addresses as they shall
appear on the records of the Company. Any notice mailed in the manner provided
herein will be conclusively presumed to have been duly given whether or not the
registered holder actually receives such notice.

         (c) The notice of redemption must specify the redemption price, the
date fixed for redemption (which must be at least 30 days after the date such
notice is mailed), the place where the Warrant certificates must be delivered
and the redemption price paid, and that the right to exercise the Warrant will
terminate at 1:30 P.M. (Phoenix, Arizona time) on the date fixed for redemption.

         (d) Appropriate adjustment shall be made to the redemption price and to
the minimum Daily Market Price prerequisite to redemption set forth in Section
10(a) hereof, in each case on the same basis as provided in Section 8 hereof
with respect to adjustment of the Warrant Price.

         (e) For purposes of this Agreement, the term "Daily Market Price" means
(i) if the Common Stock is quoted on the Nasdaq National Market or the Nasdaq
SmallCap Market or on a national securities exchange, the daily per share
closing price of the Common Stock as quoted on the Nasdaq National Market or the
Nasdaq SmallCap Market or on the principal stock exchange on which it is listed
on the trading day in question, as the case may be, whichever is the higher, or
(ii) if the Common Stock is traded in the over-the-counter market and not quoted
on the Nasdaq National Market or the Nasdaq SmallCap Market nor on any national
securities exchange, the closing bid price of the Common Stock on the trading
day in question, as reported by Nasdaq or an equivalent generally accepted
reporting service. The closing price referred to in clause (i) above shall be
the last reported sale price or, in case no such reported sale takes place on
such day, the average of the reported closing bid and asked prices, in either
case on the Nasdaq National Market or the Nasdaq SmallCap Market or on the
national securities exchange on which the Common Stock is then listed. For
purposes of clause (ii) above, if trading in the Common Stock is not reported by
Nasdaq, the bid price referred to in said clause shall be the lowest bid price
as quoted on the OTC Bulletin Board or reported in the "pink sheets" published
by National Quotation Bureau, Incorporated.

         (f) On the redemption date, each Warrant will be automatically
converted into the right to receive the redemption price and the Company will no
longer honor any purported exercise of a Warrant. On or before the redemption
date, the Company will deposit sufficient funds for the purpose of redeeming all
of the outstanding unexercised Warrants in an interest-bearing, segregated
account for payment to holders of Warrants upon surrender of Warrant
Certificates in exchange for the redemption price therefor. Funds remaining in
such account on the date three years from the redemption date will be returned
to the Company.

         Section 11. RIGHTS AS WARRANTHOLDERS. Nothing contained in this
Agreement or in any of the Warrants shall be construed as conferring upon the
holders thereof, as such, any of the rights of stockholders of the Company,
including, without limitation, the right to receive dividends or other


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distributions, to exercise any preemptive rights, to vote or to consent or to
receive notice as stockholders in respect of the meetings of stockholders or the
election of directors of the Company or any other matter.

         Section 12.       RESTRICTIONS ON TRANSFER; REGISTRATION RIGHTS.

         (a) Each holder of a Warrant agrees that prior to making any
disposition or transfer of the Warrants or shares issuable upon exercise of the
Warrants ("Shares"), unless a registration statement under the Securities Act of
1933, as amended (the "Securities Act"), is in effect with regard thereto and
the disposition may be effected in accordance therewith and with applicable
state securities laws, the holder shall give written notice to the Company
describing briefly the manner in which any such proposed disposition or transfer
is to be made; and no such disposition shall be made except pursuant to an
exemption from the registration requirements of all applicable federal and state
securities laws.

         (b) Each certificate evidencing the Warrants shall bear a legend in
substantially the following form, and each certificate evidencing Shares
issuable upon exercise of the Warrants shall bear such a legend until such time
as such Shares have been sold pursuant to a registration statement contemplated
in subsection (c) or (d) below or unless, in the opinion of legal counsel to the
Company, such legend is not required in order to establish compliance with any
provisions of applicable security laws:

                  THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
                  REGISTERED UNDER THE SECURITIES ACT OF 1933 OR ANY STATE
                  SECURITIES LAWS AND MAY NOT BE SOLD, EXCHANGED, HYPOTHECATED
                  OR OTHERWISE TRANSFERRED IN ANY MANNER EXCEPT IN COMPLIANCE
                  WITH SECTION 12 OF THE WARRANT AGREEMENT DATED AS OF FEBRUARY
                  12, 1998, AS THE SAME MAY BE AMENDED FROM TIME TO TIME.

         (c) Subject to the next sentence below, beginning on the date that the
Warrants are exercised, if the Company proposes to file with the Commission a
registration statement with respect to equity securities of the Company (other
than as to securities issued pursuant to an employee benefit plan or as to a
transaction subject to Rule 145 promulgated under the Securities Act or for
which a Form S-4 Registration Statement could be used), it shall, at least 30
days prior to such filing, give written notice of such proposed filing to the
holders of Warrants and Shares which bear a legend as contemplated in Section
12(b) above and which shall not have previously been included in a registration
statement filed under this Section 12(c) or Section 12(d), at their respective
addresses as they appear on the records of the Company or the Company, and shall
offer to include and shall include, subject to the provisions of this Section
12(c), in such filing any proposed disposition of such Shares upon receipt by
the Company, not less than 10 days prior to the proposed filing date, of a
request therefor setting forth the facts with respect to such proposed
disposition and all other


                                       11

<PAGE>   12



information with respect to the holders of such Shares requested to be included
in such filing as shall be reasonably necessary to be included in such
Registration Statement. Notwithstanding the above, after such time as the
holders shall have been given two opportunities to include their Shares in a
Registration Statement of the Company pursuant to the immediately preceding
sentence, and all securities of holders who shall have requested such inclusion
in accordance herewith and who have not withdrawn such request prior to the
filing of such Registration Statement have been included in such a Registration
Statement which shall have become effective and such securities shall have been
effectively registered under the Securities Act, the Company will have no
further obligation to such holders under this Section 12(c) and the Shares of
such holders that have not been included previously in a Registration Statement
under this Section 12(c) will have no further registration rights under Section
12(c) of this Agreement. In the event that (i) the managing underwriter for any
such offering advises the Company in writing that the inclusion of such Shares
in the offering would be detrimental to the offering or (ii) in the event that
there is no managing underwriter, if, in the good faith judgment of the Board of
Directors of the Company, inclusion of the Shares in the registration would be
seriously detrimental to the Company, then, such Shares shall not be included in
the Registration Statement, provided that no other shares of the Company's
Common Stock are included in the registration pursuant to any other piggyback
registration rights granted to others. In the event that Shares requested to be
included in an offering are not included in accordance with the immediately
preceding sentence, any notice given to holders of Warrants and Shares hereunder
with respect to such offering shall not be counted against the limitation
provided for in the second sentence of this Section 12(c).

         (d) In addition to any Registration Statement pursuant to Section 12(c)
hereof, after written notice upon exercise (the "Request") by the holders of at
least 50% of the shares of Common Stock which have been (or may be) issued upon
exercise of the Warrants, the Company will, as promptly as practicable (but in
any event within 60 days), prepare and file at its own expense a Registration
Statement with the Commission and appropriate Blue Sky authorities sufficient to
permit the public offering of the shares of Common Stock underlying the
Warrants, and will use reasonable efforts at its own expense through its
officers, directors, auditors and counsel, in all ways necessary or advisable,
to cause such Registration Statement to become effective as quickly as
practicable and to maintain such effectiveness so as to permit resale of the
shares of Common Stock covered by the Request until the earlier of the time that
all such shares of Common Stock has been sold or the expiration of 120 days from
the effective date of the Registration Statement; provided, however, that the
Company shall only be obligated to file one such Registration Statement under
this Section 12(d). The Company shall not be required to effect a registration
pursuant to this Section 12(d) if the Company shall furnish to holders
requesting a registration statement pursuant to this Section 12(d), a
certificate signed by the Chairman of the Board stating that in the good faith
judgment of the Board of Directors of the Company, it would be seriously
detrimental to the Company and its shareholders for such registration statement
to be effected at such time, in which event the Company shall have the right to
defer such filing for a period of not more than ninety (90) days after receipt
of the request of the initiating holders; provided that such right to delay a
request shall be exercised by the Company not more than once in any twelve (12)
month period.



                                       12

<PAGE>   13



         (e) All fees, disbursements, and out-of-pocket expenses incurred in
connection with the filing of any Registration Statement under Section 12(c)
hereof and in complying with applicable securities and Blue Sky laws shall be
borne by the Company, provided, however, that any expenses of the holders of the
Warrants or the Shares, including but not limited to attorneys' fees and
discounts and commissions, shall be borne by such holders. The Company at its
expense will supply the holders of the Shares included in a Registration
Statement with copies of such Registration Statement and the prospectus or
offering circular included therein in such quantities as may be reasonably
requested by such holders.

         (f) Each holder of Shares to be included in a Registration Statement
pursuant to this Section 12 agrees to reasonably cooperate with the Company and
to provide the Company on its request with all information concerning such
holder and his Warrants and Shares that may reasonably be requested by the
Company in order for the Company to perform its obligations under this Section
12.

         (g) The registration rights provided pursuant to Section 12(c) and
Section 12(d) above are subject to certain registration rights granted to
SunAmerica Life Insurance Company and its assignees pursuant to that certain
Amended and Restated Registration Rights Agreement entered into as of June 21,
1996 between the Company and SunAmerica Life Insurance Company. Specifically,
the Amended and Restated Registration Rights Agreement entered into as of June
21, 1996 provides that the holders of registrable securities under that
agreement shall have the right to have included in any piggyback registration by
the Company any registrable securities requested by them to be so included in
such piggyback registration prior to the inclusion of any securities requested
to be registered by any third parties entitled to any other registration rights,
including the registration rights granted hereunder.

         Section 13.       INDEMNIFICATION.

         (a) In the event of the filing of any Registration Statement with
respect to the Shares pursuant to Section 12 above, the Company agrees to
indemnify and hold harmless the holders of such Shares (for purposes of this
Section 13, references to any holder of Shares shall refer only to such holders
who have agreed to be bound by this Section 13), and each person who controls
such holders within the meaning of the Securities Act and such holders'
officers, directors, managers, members, partners, and principle equity holders
(collectively, "Indemnitees") against all losses, claims, damages, expenses and
liabilities, joint or several (which shall, for all purposes of this Agreement,
include, but not be limited to, all costs of defense and investigation and all
attorneys' fees and expenses), to which such Indemnitees may become subject,
under the Securities Act or otherwise, insofar as such losses, claims, damages,
expenses or liabilities (or actions in respect thereof) arise out of or are
based upon any untrue statement or alleged untrue statement of any material fact
contained in any such Registration Statement, or any related preliminary
prospectus, final prospectus, offering circular, notification or amendment or
supplement thereto, or arise out of or are based upon the omission or alleged
omission to state therein a material fact required to be stated therein or
necessary to make the statements therein, in the light of the circumstances in
which


                                       13

<PAGE>   14



they were made, not misleading; provided, however, that the Company will not be
liable in any such case to the extent that any such loss, claim, damage,
expenses, or liability arises out of or is based upon an untrue statement or
alleged untrue statement or omission or alleged omission made in such
Registration Statement, preliminary prospectus, final prospectus, offering
circular, notification or amendment or supplement thereto in reliance upon, and
in conformity with, written information furnished to the Company by any such
holder specifically for use in the preparation thereof and, provided further,
that the indemnity agreement provided in this Section 13(a) with respect to any
preliminary prospectus shall not inure to the benefit of any holder of Warrants
or Shares from whom the person asserting any losses, claims, damages,
liabilities or actions based upon any untrue statement or alleged untrue
statement of material fact or omission or alleged omission to state therein a
material fact purchased Warrants or Shares, if a copy of the prospectus in which
such untrue statement or alleged untrue statement or omission or alleged
omission was corrected had not been sent or given to such person within the time
required by the Securities Act and the rules and regulations thereunder, unless
such failure is the result of non-compliance by the Company with the last
sentence of Section 12(f) hereof. This indemnity will be in addition to any
liability which the Company may otherwise have.

         (b) Each holder of a Warrant and each holder of a Share agrees that he
will indemnify and hold harmless the Company, each other person referred to in
subparts (1), (2) and (3) of Section 11(a) of the Securities Act in respect of
the Registration Statement, each officer of the Company, and each person who
controls the Company within the meaning of the Securities Act, against any
losses, claims, damages or liabilities (which shall, for all purposes of this
Agreement, include, but not be limited to, all costs of defense and
investigation and all attorneys' fees) to which the Company or any such
director, officer or controlling person may become subject under the Securities
Act or otherwise, insofar as such losses, claims, damages or liabilities (or
actions in respect thereof) arise out of or are based upon any untrue statement
or alleged untrue statement of any material fact contained in any such
Registration Statement, or any related preliminary prospectus, final prospectus,
offering circular, notification or amendment or supplement thereto, or arise out
of or are based upon the omission or alleged omission to state therein a
material fact required to be stated therein or necessary to make the statements
therein not misleading, but in each case only to the extent that such untrue
statement or alleged untrue statement or omission or alleged omission was made
in such Registration Statement, preliminary prospectus, final prospectus,
offering circular, notification or amendment or supplement thereto in reliance
upon, and in conformity with, written information furnished to the Company by
such holder specifically for use in the preparation thereof. This indemnity will
be in addition to any liability which the holder may otherwise have.

         (c) Promptly after receipt by an indemnified party under this Section
13 of notice of the commencement of any action, such indemnified party will, if
a claim in respect thereof is to be made against the indemnifying party under
this Section 13, notify the indemnifying party of the commencement thereof. No
indemnification provided for in this Section 13 shall be available to any party
who shall fail to give the notice to the extent the party to whom such notice
was not given was materially prejudiced by the failure to give the notice, but
the omission so to notify the indemnifying party will not relieve the
indemnifying party or parties from any liability which it may have to any


                                       14

<PAGE>   15



indemnified party for contribution otherwise than as to the particular item as
to which indemnification is then being sought solely pursuant to this Section
13. In case any such action is brought against any indemnified party, and it
notifies the indemnifying party of the commencement thereof, the indemnifying
party will be entitled to participate in, and, to the extent that it may wish,
jointly with any other indemnifying party similarly notified, reasonably assume
the defense thereof, subject to the provisions herein stated and after notice
from the indemnifying party to such indemnified party of its election so to
assume the defense thereof, the indemnifying party will not be liable to such
indemnified party under this Section 13 for any legal or other expenses
subsequently incurred by such indemnified party in connection with the defense
thereof other than reasonable costs of investigation unless the indemnifying
party shall not pursue the action to its final conclusion. The indemnified party
shall have the right to employ separate counsel in any such action and to
participate in the defense thereof, but the fees and expenses of such counsel
shall not be at the expense of the indemnifying party. No settlement of any
action against an indemnified party shall be made without the consent of the
indemnifying party, which shall not be unreasonably withheld in light of all
factors of importance to such indemnified party.

         Section 14. NOTICES. Notices or demands authorized by this Agreement to
be given or made by the holder of any Warrant certificate to or on the Company
shall be sufficiently given or made if sent by registered or certified mail,
addressed as follows (and shall be deemed given upon receipt):

                           Ugly Duckling Corporation
                           2525 East Camelback Road
                           Suite 1150
                           Phoenix, Arizona 85016
                           Attention:  Steven P. Johnson, Senior Vice President,
                                       General Counsel and Secretary

                           With a copy to:

                           Steven D. Pidgeon
                           Snell & Wilmer L.L.P.
                           One Arizona Center
                           Phoenix, Arizona 85004-0001

Notices or demands authorized by this Agreement to be given or made by the
Company to the holder of any Warrant certificate shall be sufficiently given or
made if sent by first class mail, postage prepaid, addressed to such holder at
the address of such holder as shown in the Warrant Register.

         Section 15. SUPPLEMENTS AND AMENDMENTS. This Agreement may be amended
by the Company and the holder or holders of a majority of the outstanding
Warrants representing a majority of the shares of Common Stock underlying such
Warrants; provided, however, that without the


                                       15

<PAGE>   16



consent of each holder of a Warrant, there can be no increase of the Warrant
Price or reduction of the exercise period for such holder's Warrants.

         Section 16. SUCCESSORS. All the covenants and provisions of this
Agreement by or for the benefit of the Company or the registered holders of the
Warrants will bind and inure to the benefit of their respective successors and
assigns hereunder.

         Section 17. GOVERNING LAW. This Agreement will be deemed to be a
contract made under the laws of the State of California and for all purposes
will be construed in accordance with the laws of said State.

         Section 18. BENEFITS OF THIS AGREEMENT. Nothing in this Agreement will
be construed to give to any person or corporation other than the Company and the
registered holders of the Warrants any legal or equitable right, remedy or claim
under this Agreement. This Agreement is for the sole and exclusive benefit of
the Company and the registered holders of the Warrants.

         Section 19. COUNTERPARTS. This Agreement may be executed in
counterparts and each of such counterparts will for all purposes be deemed to be
an original, and all such counterparts will together constitute but one and the
same instrument.

         Section 20. DESCRIPTIVE HEADINGS. The descriptive headings of the
several Sections of this Agreement are inserted for convenience only and do not
control or affect the meaning or construction of any of the provisions hereof.




                                       16

<PAGE>   17




         IN WITNESS WHEREOF, the parties have caused this Agreement to be duly
executed, as of the day and year first above written.

                        UGLY DUCKLING CORPORATION
 
                        By: /s/ Steven P. Johnson
                        Name: Steven P. Johnson
                        Its: Senior Vice President and General Counsel


                        ARBCO ASSOCIATES, L.P.

                        By: KAIM Non-Traditional, L.P.
                        Its: General Partner

                        By: Kayne Anderson Investment Management, Inc.
                        Its: General Partner

                        By: /s/ Richard A. Kayne
                           ___________________________________
                        Title:  Authorized Officer
                              ________________________________

                                 Address for notices:
                                 1800 Avenue of the Stars, Suite 200
                                 Los Angeles, CA 90067

                                 Attn:
                                 Telephone:  (310) 284-6483
                                 Telecopy :  (310) 284-6444

                        KAYNE ANDERSON NON-TRADITIONAL
                        INVESTMENTS, L.P.

                        By: Kayne Anderson Non-Traditional, L.P.
                        Its: General Partner

                        By: Kayne Anderson Investment Management, Inc.
                        Its: General Partner


                        By: /s/ Richard A. Kayne
                           ___________________________________
                        Name:   Richard A. Kayne
                             _________________________________
                        Title:  Authorized Officer
                              ________________________________

                                 Address for notices:
                                 1800 Avenue of the Stars, Suite 200
                                 Los Angeles, CA 90067
                                 Attn:
                                 Telephone: (310) 284-6438
                                 Telecopy:   (310) 284-6444


                                       17

<PAGE>   18




                                  OFFENSE GROUP ASSOCIATES, L.P.
                                  By: Kayne Anderson Non-Traditional, L.P.
                                  Its: General Partner

                                  By: Kayne Anderson Investment Management, Inc.
                                  Its: General Partner

                                  By: /s/ RICHARD A. KAYNE
                                     _________________________________
                                  Name:   Richard A. Kayne
                                       ______________________________
                                  Title:  Authorized Officer
                                        ________________________________

                                           Address for notices:
                                           1800 Avenue of the Stars, Suite 200
                                           Los Angeles, CA 90067

                                           Attn:
                                           Telephone:  (310) 284-6483
                                           Telecopy :  (310) 284-6444


                                  OPPORTUNITY ASSOCIATES,
                                  LIMITED PARTNERSHIP

                                  By: Kayne Anderson Non-Traditional, L.P.
                                  Its: General Partner

                                  By: Kayne Anderson Investment Management, Inc.
                                  Its: General Partner


                                  By: /s/ RICHARD A. KAYNE
                                     _____________________________
                                  Name:   Richard A. Kayne
                                       __________________________
                                  Title:  Authorized Officer
                                        ____________________________

                                           Address for notices:
                                           1800 Avenue of the Stars, Suite 200
                                           Los Angeles, CA 90067
                                           Attn:
                                           Telephone: (310) 284-6438
                                           Telecopy:   (310) 284-6444





                                       18

<PAGE>   19



                              KAYNE ANDERSON OFFSHORE LIMITED


                              By:    /s/  John Sutlic              
                                     ------------------------------
                              Name:  John Sutlic                    
                              Title: Authorized Officer              

                                       Address for notices:
                                       1800 Avenue of the Stars, Suite 200
                                       Los Angeles, CA 90067
                                       Attn:
                                       Telephone: (310) 284-6438
                                       Telecopy:   (310) 284-6444

                              GLACIER WATER SERVICES, INC.


                              By:    /s/  Jerry Welch                  
                                     ------------------------------
                              Name:  Jerry Welch                  
                              Title: Authorized Officer             

                                       Address for notices:
                                       1800 Avenue of the Stars, Suite 200
                                       Los Angeles, CA 90067
                                       Attn:
                                       Telephone: (310) 284-6438
                                       Telecopy:   (310) 284-6444

                              PARADIGM INSURANCE COMPANY


                              By:    /s/  Frank Arkfeld            
                                     ------------------------------
                              Name:  Frank Arkfeld                  
                              Title: Authorized Officer              

                                       Address for notices:
                                       1800 Avenue of the Stars, Suite 200
                                       Los Angeles, CA 90067
                                       Attn:
                                       Telephone: (310) 284-6438
                                       Telecopy:   (310) 284-6444

                              FOREMOST INSURANCE COMPANY


                              By:    /s/ Donald Welsh                
                                     ------------------------------
                              Name:  Donald Welsh
                              Title: Authorized Officer            

                                       Address for notices:
                                       1800 Avenue of the Stars, Suite 200
                                       Los Angeles, CA 90067
                                       Attn:
                                       Telephone: (310) 284-6438
                                       Telecopy:   (310) 284-6444

                              TOPA INSURANCE COMPANY


                              By:    /s/  Nosh Marfatia              
                                     ------------------------------
                              Name:  Nosh Marfatia 
                              Title: Authorized Officer 

                                       Address for notices:
                                       1800 Avenue of the Stars, Suite 200
                                       Los Angeles, CA 90067
                                       Attn:
                                       Telephone: (310) 284-6438
                                       Telecopy:   (310) 284-6444



                                       19
<PAGE>   20
                                   EXHIBIT A

Warrant No.  ____



               WARRANT TO PURCHASE ________ SHARES OF COMMON STOCK

                              VOID AFTER 1:30 P.M.,
                   PHOENIX, ARIZONA TIME, ON FEBRUARY 12, 2001
                       OR SUCH LATER DATE SET FORTH HEREIN

                            UGLY DUCKLING CORPORATION

         This certifies that, for value received ________________________, the
registered holder hereof or assigns (the "Holder"), is entitled to purchase from
UGLY DUCKLING CORPORATION, a Delaware corporation (the "Company"), at any time
after February 12, 1998, and before the later of (i) 1:30 p.m., Phoenix, Arizona
time, on February 12, 2001 or (ii) such time as the Company has repaid in full
its Notes issued pursuant to that certain Loan Agreement dated as of February
12, 2001 between the Company and each of the Lenders named therein, at the
purchase price per share of $10.00 (the "Warrant Price"), the number of shares
of Common Stock, par value $0.001 per share, of the Company set forth above (the
"Shares"). The number of shares of Common Stock purchasable upon exercise of the
Warrant evidenced hereby and the Warrant Price is subject to adjustment from
time to time as set forth in the Warrant Agreement referred to below.

         This Warrant may be redeemed, at the option of the Company and as more
specifically provided in the Warrant Agreement, at $.10 per share of Common
Stock purchasable upon exercise hereof, at any time after the average Daily
Market Price (as defined in Section 10 of the Warrant Agreement) per share of
the Common Stock for a period of at least twenty (20) consecutive trading days
ending not more than fifteen days prior to the date of the notice given pursuant
to Section 10(b) thereof has equaled or exceeded $16.00, and prior to expiration
of this Warrant. The Holder's right to exercise this Warrant terminates at 1:30
p.m. (Phoenix, Arizona time) on the date fixed for redemption in the notice of
redemption delivered by the Company in accordance with the Warrant Agreement.

         The Warrants evidenced hereby may be exercised during the period
referred to above, in whole or in part, by presentation of this Warrant
certificate with the Purchase Form attached hereto duly executed and guaranteed
and simultaneous payment of the Warrant Price (as defined in the Warrant
Agreement and subject to adjustment as provided therein) at the principal office
of the Company. Payment of such price may be made at the option of the Holder in
cash or by certified check or bank draft, all as provided in the Warrant
Agreement.

         The Warrants evidenced hereby are part of a duly authorized issue of
Warrants and are issued under and in accordance with the Warrant Agreement dated
as of February 12, 1998, between the


                                       1

<PAGE>   21



Company and the Lenders party thereto, and are subject to the terms and
provisions contained in such Warrant Agreement, which Warrant Agreement is
hereby incorporated by reference herein and made a part hereof and is hereby
referred to for a description of the rights, limitations, duties and indemnities
thereunder of the Company and the Holder of the Warrants, and to all of which
the Holder of this Warrant certificate by acceptance hereof consents. A copy of
the Warrant Agreement may be obtained for inspection by the Holder hereof upon
written request to the Company.

         Upon any partial exercise of the Warrants evidenced hereby, there will
be issued to the Holder a new Warrant certificate in respect of the Shares
evidenced hereby that have not been exercised. This Warrant certificate may be
exchanged at the office of the Company by surrender of this Warrant certificate
properly endorsed either separately or in combination with one or more other
Warrants for one or more new Warrants to purchase the same aggregate number of
Shares as evidenced by the Warrant or Warrants exchanged. No fractional Shares
will be issued upon the exercise of rights to purchase hereunder, but the
Company will pay the cash value of any fraction upon the exercise of one or more
Warrants, as provided in the Warrant Agreement.

         The Warrant Price and the number of shares of Common Stock issuable
upon exercise of this Warrant is subject to adjustment as provided in Section 8
of the Warrant Agreement. The Warrant Agreement may be amended by the Company
and the holder or holders of a majority of the outstanding Warrants representing
a majority of the shares of Common Stock underlying such Warrants; provided that
without the consent of each holder of a Warrant certain specified changes cannot
be made to such holder's Warrants.

         Neither the Warrants nor the shares of Common Stock underlying the
Warrants may be sold, assigned, or otherwise transferred except in accordance
with the provisions of the Warrant Agreement.

         The Holder hereof may be treated by the Company and all other persons
dealing with this Warrant certificate as the absolute owner hereof for all
purposes and as the person entitled to exercise the rights represented hereby,
any notice to the contrary notwithstanding, and until any transfer is entered on
such books, the Company may treat the Holder hereof as the owner for all
purposes. Notices and demands to be given to the Company must be given by
certified or registered mail at the addresses provided in the Warrant Agreement.

         All terms used in the Warrant Certificate that are defined in the
Warrant Agreement shall have the respective meanings ascribed to such terms in
the Warrant Agreement.

Dated:                                                 UGLY DUCKLING CORPORATION

                                                       By:





                                       2
<PAGE>   22
\                            UGLY DUCKLING CORPORATION
                                  PURCHASE FORM

                                Mailing Address:
                            UGLY DUCKLING CORPORATION
                            2525 East Camelback Road
                                   Suite 1150
                             Phoenix, Arizona 85016

         The undersigned hereby irrevocably elects to exercise the right of
purchase represented by the within Warrant certificate for, and to purchase
thereunder, _____________Shares of Common Stock provided for therein, and
requests that certificates for such Shares be issued in the name of:


(Please Print or Type Name, Address and Social Security Number)

and that such certificates be delivered to                              
whose address is                                                            
and, if said number of Shares shall not be all the Shares purchasable hereunder,
that a new Warrant certificate for the balance of the Shares purchasable under
the within Warrant certificate be registered in the name of the undersigned
Holder or his or her Assignee as below indicated and delivered to the address
stated below.

                                                              Dated:
Name of Holder or Assignee:


(Please Print)

Address:


Signature:


NOTE: The above signature must correspond with the name as it appears upon the
face of the within Warrant certificate in every particular, without alteration
or enlargement or any change whatever, unless these Warrants have been assigned.

Signature Guaranteed:


THE SIGNATURE(S) SHOULD BE GUARANTEED BY AN ELIGIBLE GUARANTOR INSTITUTION
(Banks, Stock Brokers, Savings and Loan Association, and Credit Unions) WITH


                                       3



<PAGE>   23



MEMBERSHIP IN AN APPROVED SIGNATURE GUARANTEE MEDALLION PROGRAM PURSUANT TO
S.E.C. RULE 17Ad-15.


                                       4


<PAGE>   24
                                   ASSIGNMENT

                 (To be signed only upon assignment of Warrants)

  FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfers unto


          (Name and Address of Assignee Must Be Printed or Typewritten)



______________ Warrants, hereby irrevocably constituting and appointing _______
Attorney to transfer said Warrants on the books of the Company, with full power
of substitution in the premises.

Dated:


                                    Signature of Registered Holder

                                    Note:   The signature on this assignment
                                            must correspond with the name as it
                                            appears upon the face of the within
                                            Warrant certificate in every
                                            particular, without alteration or
                                            enlargement or any change whatever.

Signature Guaranteed:



THE SIGNATURE(S) SHOULD BE GUARANTEED BY AN ELIGIBLE GUARANTOR
INSTITUTION (Banks, Stock Brokers, Savings and Loan Association, and Credit
Unions) WITH MEMBERSHIP IN AN APPROVED SIGNATURE GUARANTEE MEDALLION PROGRAM
PURSUANT TO S.E.C. RULE 17Ad-15.




                                       5

<PAGE>   25
                                    EXHIBIT B



                             ALLOCATION OF WARRANTS


<TABLE>
<CAPTION>
         Name of Lender                 Warrants
         --------------                 --------
<S>                                     <C>        
ARBCO Associates, L.P.                    90,000

Kayne Anderson Non-Traditional
Investments, L.P.                        100,000

Offense Group Associates, L.P.            80,000

Opportunity Associates, Limited
Partnership                               30,000

Kayne Anderson Offshore Limited           10,000

Glacier Water Services, Inc.              70,000

Paradigm Insurance Company                40,000

Foremost Insurance Company                50,000

Topa Insurance Company                    30,000
                                         -------

                                         500,000
</TABLE>