
<PAGE>   1
                                                                 Exhibit 10.25.3

                                December 4, 1998



<TABLE>
<S>                            <C>                          <C>
BALLET LIMITED                  EQUITY CSKA LIMITED           SOUTH BAY LIMITED
DENARY LIMITED                  EQUITY CSKB LIMITED           NEW CSK EQUITY LIMITED
GLEAM LIMITED                   AUTO EQUITY LIMITED           CHASE BANK (C.I.)
HIGHLANDS LIMITED               AUTO PARTS LIMITED                  NOMINEES LIMITED
NOBLE LIMITED                   AUTO INVESTMENTS              THE JAB TRUST
OUTRIGGER LIMITED                     LIMITED                 James G. Bazlen
QUILL LIMITED                   CSK INVESTMENTS LIMITED       Maynard Jenkins
RADIAL LIMITED                  CSK EQUITY LIMITED            CHILTERN TRUSTEES
SHORELINE LIMITED               CSK INTERNATIONAL                   LIMITED (as trustee for the
ZINNIA LIMITED                        LIMITED                       Carmel Trust)
INVESTCORP INVESTMENTS          EQUITY CSKC LIMITED           TRANSATLANTIC FINANCE
    EQUITY LIMITED              INVESTCORP CSK HOLDINGS             LTD.
                                      L.P.
</TABLE>



         Re:      Stockholders' Agreement, dated October 30, 1996, by and among
                  CSK Auto Corporation (the "Company") and the stockholders
                  signatory thereto, as amended (the "Stockholders Agreement").

Ladies and Gentlemen:

         On November 13, 1998, the Company filed a Registration Statement on
Form S-1 (the "Registration Statement") covering the public offering of up to
8,050,000 shares (including the underwriters' overallotment option) of the
Company's common stock, par value $0.01 (the "Common Stock"). Capitalized terms
used but not defined herein have the meanings given to them in the Stockholders
Agreement.

         Each of you has certain registration rights with respect to shares of
the capital stock of the Company. By signing this letter agreement, each of you
waives (a) any requirement of notice under Sections 9.1 and 9.2 of the
Stockholders Agreement with respect to the registration of shares of Common
Stock contemplated by the Registration Statement, provided you are permitted to
include in the Registration Statement a number shares of Common Stock which is
not, without your written consent, materially different (other than to allow for
the exercise of the underwriters' overallotment option) from the number of
shares of Common Stock disclosed as being sold by you in the "Principal and
Selling Stockholders" section of Amendment No. 1 to the Registration Statement,
and in any case, is a pro rata amount of the total shares sold in the offering,
and (b) the right to select the managing underwriter with respect to such
offering, provided such managing underwriter is Donaldson, Lufkin & Jenrette
Securities Corporation.
<PAGE>   2
         In order to commence the public offering process, one of you was
required to "demand" a registration of shares to commence this process. By
signing this letter agreement, the Investcorp Group acknowledges that one of its
members has made such a demand in consideration of the agreement of the members
of the Carmel Group as follows:

         The members of the Carmel Group shall not make more than than three
         requests, in the aggregate, that the Company register Registrable Stock
         pursuant to Section 9.1(b) of the Stockholders Agreement (a "Demand
         Registration Request"), except with the written consent of a majority
         of the members of the Investcorp Group. A member of the Carmel Group
         shall exercise, or be deemed to have exercised, one of its four Demand
         Registration Requests the next time both the Investcorp Group and the
         Carmel Group participate in a registered offering of Registrable Stock
         through the exercise of a Demand Registration Request, after which the
         restriction contained in the immediately preceding sentence shall be of
         no further force or effect.

By signing this letter agreement, the members of the Carmel Group hereby
acknowledge and memorialize such agreement.

         Finally, by signing this letter agreement, each of you acknowledges
that you are participating in the offering pursuant to a demand registration
right (in the case of members of the Investcorp Group) or a piggyback
registration right (in the case of members of the Carmel Group), and that each
of you is including in the offering the number of shares of common stock set
forth opposite your respective name in Exhibit A hereto.

         Please sign in the space provided below to indicate your acceptance of
the terms of this letter agreement. This letter agreement may be executed in
counterpart, and shall be a binding agreement among each party signatory hereto.



                                   Sincerely,

                                    CSK AUTO CORPORATION

                                    By:      ______________________
                                    Name:    ______________________
                                    Title:   ______________________

                                    CSK AUTO, INC.

                                     By:      ______________________
                                     Name:    ______________________
                                     Title:   ______________________


                                       2
<PAGE>   3
AGREED AND ACCEPTED:

BALLET LIMITED                                  Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

DENARY LIMITED                                  Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

GLEAM LIMITED                                   Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

HIGHLANDS LIMITED                               Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

NOBLE LIMITED                                   Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

OUTRIGGER LIMITED                               Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

QUILL LIMITED                                   Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

RADIAL LIMITED                                  Executed on:  December __, 1998

By:      ___________________________

                                       3
<PAGE>   4
         Name:
         Title:

SHORELINE LIMITED                               Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

ZINNIA LIMITED                                  Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

INVESTCORP INVESTMENTS EQUITY LIMITED           Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

EQUITY CSKA LIMITED                             Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

EQUITY CSKB LIMITED                             Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

AUTO EQUITY LIMITED                             Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

AUTO PARTS LIMITED                              Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

AUTO INVESTMENTS LIMITED                        Executed on:  December __, 1998

                                       4
<PAGE>   5
By:      ___________________________
         Name:
         Title:

CSK INVESTMENTS LIMITED                         Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

CSK EQUITY LIMITED                              Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

CSK INTERNATIONAL LIMITED                       Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

EQUITY CSKC LIMITED                             Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

INVESTCORP CSK HOLDINGS L.P.                    Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

SOUTH BAY LIMITED                               Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

NEW CSK EQUITY LIMITED                          Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:


                                       5
<PAGE>   6
CHASE BANK (C.I.) NOMINEES LIMITED              Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:

THE JAB TRUST                                   Executed on:  December __, 1998

By:      ___________________________
         Name:  James G. Bazlen
         Title:  Trustee

By:      ___________________________
         Name:  Alice T. Bazlen
         Title:  Trustee

                                                Executed on:  December __, 1998

____________________________________
James G. Bazlen

                                                Executed on:  December __, 1998

_____________________________________
Maynard Jenkins

CHILTERN TRUSTEES LIMITED, in its capacity as   Executed on:  December __, 1998
trustee for The Carmel Trust

By:      ___________________________
         Name:
         Title:

TRANSATLANTIC FINANCE LTD.                      Executed on:  December __, 1998

By:      ___________________________
         Name:
         Title:


                                       6
