<PAGE>   1

                                                                    EXHIBIT 4.6





                                                                January 17, 1995

The Lenders (as defined below)

                 and

Societe Generale, as Agent
1221 Avenue of Americas
New York, New York 10019

Attention:  David I. Brunson

                 Re:      Letter of Understanding Regarding Amended
                          and Restated Stockholders Agreement

Dear Sirs:

         Reference is made to (a) the Credit and Guaranty Agreement, dated as
of January 17, 1995 (together with all amendments and modifications thereto
from time to time, the "Credit Agreement"), among E-Z Serve Convenience Stores,
Inc., a Delaware corporation (the "Borrower"), E-Z Serve Corporation, a
Delaware corporation (the "Parent"), the various financial institutions as are
or may become parties thereto (collectively, the "Lenders") and Societe
Generale ("SG"), as agent (in such capacity, the "Agent") for the Lenders and
(b) the Amended and Restated Stockholders Agreement, dated as of June 1, 1994
(the "Stockholders Agreement"), among the Parent, DLJ Capital Corporation,
Phemus Corporation, Tenacqco Bridge Partnership, Intercontinental Mining &
Resources Incorporated, Quadrant Capital Corp. (collectively, the
"Stockholders") and certain employees of the Parent.

         In order to induce the Lenders and the Agent to execute the Credit
Agreement and consummate the transactions contemplated thereby, and for other
good and valuable consideration, the receipt and adequacy of which is hereby
acknowledged, the Stockholders and the Parent (each, an "Agreeing Party") each
severally, but not jointly, agree to the following:

                 1.  Notwithstanding any term or provision thereof to the
         contrary, including Section 4.1 thereof, the Stockholders Agreement,
         as modified hereby and as it applies to the Stockholders, shall not
         terminate and shall remain in full force and effect until all
         obligations (monetary or otherwise) of the Parent and each of its
         Subsidiaries (including without limitation the Borrower) arising under
         or
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         in connection with the Credit Agreement, the Notes issued thereunder
         (the "Notes") and each other Loan Document executed pursuant thereto
         (including without limitation as to letters of credit ("Letters of
         Credit")) have been paid in cash in full and all Commitments (as
         defined in the Credit Agreement) have expired or terminated;

                 2.  Each Agreeing Party agrees that it will not (a) amend,
         supplement or otherwise modify the Stockholders Agreement without the
         prior written consent of the Agent, which consent shall not be
         unreasonably withheld, or (b) amend, supplement or otherwise modify
         this Letter of Understanding without the prior written consent of the
         Agent;

                 3.  Notwithstanding any term or provision of the Stockholders
         Agreement (including without limitation any permissions, exceptions,
         rights to compel, tag along rights and buy-sell rights contained
         therein), each Stockholder agrees that it will not sell, offer or
         otherwise Transfer (as defined in the Stockholders Agreement) any
         shares of Common Stock (as defined in the Stockholders Agreement) or
         Options (as defined in the Stockholders Agreement) if, as a result of
         such action, such Holder (as defined in the Stockholders Agreement)
         would at any time (a) be entitled to cast less than 70% of the votes
         the number of fully-diluted shares of Common Stock set forth opposite
         its name on Schedule I attached to the Stockholders Agreement carries
         or (b) have ownership and control, free and clear of all liens,
         security interests and other encumbrances (other than non-consensual
         liens and encumbrances that arise by operation of law and that would
         not reasonably be expected to result in a Transfer of such Common
         Stock), of less than 70% of the number of fully-diluted shares of
         Common Stock set forth opposite its name on Schedule I attached to the
         Stockholders Agreement, in each case without the prior written consent
         of the Agent;

                 4.  Subject to paragraph 3 above, each Stockholder agrees that
         it will maintain its ownership interest in the Parent without any
         lien, security interest or other encumbrance thereon, in whole or in
         part (other than non-consensual liens and encumbrances that arise by
         operation of law and that would not reasonably be expected to result
         in a Transfer of such Common Stock);

                 5.  Such Agreeing Party will strictly comply with all
         provisions of the Stockholders Agreement, as modified hereby, and in
         any event any attempt by a Holder to Transfer any shares of Common
         Stock or Options not in compliance with





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         the Stockholders Agreement, as modified hereby, shall be null and
         void;

                 6.  The Parent shall maintain a copy of this letter agreement
         together with the Stockholders Agreement at its executive office and
         its registered office in the State of Delaware and shall comply with
         any other requirements, if any, applicable to this letter agreement
         under the Delaware General Corporation Law and, in any event, each
         Stockholder agrees that it shall duly legend its shares of Common
         Stock with a legend to the effect that such shares are subject to this
         letter and shall supply the Agent with satisfactory evidence thereof
         within 10 days after the date hereof; and

                 7.  Each Agreeing Party hereby represents and warrants that
         (a) this letter agreement constitutes a legal, valid and binding
         obligation of such Agreeing Party, enforceable in accordance with its
         terms, except as enforcement may be limited by bankruptcy, insolvency,
         moratorium and other similar laws affecting the rights of creditors
         generally and except for limitations imposed by general principles of
         equity and (b) the Stockholders Agreement has become effective and is
         in full force and effect.

         This letter agreement constitutes a Loan Document (as defined in the
Credit Agreement) and, notwithstanding the provisions of Section 4.8 of the
Stockholders Agreement, shall inure to the benefit of the Agent and the
Lenders.  The parties hereto acknowledge that any breach of this letter
agreement or the Stockholders Agreement will result in an immediate Event of
Default under the Credit Agreement.  The parties hereto hereby further agree
that money damages would not be a sufficient remedy for any breach of this
letter agreement and that the Agent shall be entitled to specific performance
and injunctive or other equitable relief as a remedy for any such breach, and
the parties hereto further agree to waive any requirement for the securing or
posting of any bond in connection with such remedy.  Such remedy shall not be
deemed to be the exclusive remedy for breach of this agreement, but shall be in
addition to all other remedies available at law or equity.  In any action or
proceeding brought to enforce any provision of this letter, the Agent, if
successful, shall be entitled to recover reasonable attorney's fees and
expenses from the party against which enforcement is sought.

         This letter is intended to create several, and not joint, obligations
and no Agreeing Party shall be responsible for any act or omission, or any
breach of a representation, warranty or covenant, by any other Agreeing Party.





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         Please acknowledge your agreement with the foregoing terms by
executing in the space provided below and delivering to the Agent a counterpart
of this letter.  This letter (together with the Stockholders Agreement)
constitutes the entire agreement and understanding of the parties hereto with
respect to the subject matter hereof and may be executed in separate
counterparts, shall be binding upon and inure to the benefit of successors and
assigns of the parties hereto AND SHALL BE GOVERNED BY, AND CONSTRUED IN
ACCORDANCE WITH, THE INTERNAL LAWS OF THE STATE OF NEW YORK.  The obligations
of the parties under this letter shall terminate when all principal and
interest on the Notes or payable under the Credit Agreement, all amounts with
respect to the Letters of Credit and all fees and expenses payable under the
Credit Agreement have been paid in full in cash and all Commitments have
expired or terminated.

                                        Very truly yours,

                                        E-Z SERVE CORPORATION


                                        By:/s/ John T. Miller             
                                           -------------------------------------
                                           Title: Senior Vice President


                                        DLJ CAPITAL CORPORATION


                                        By:/s/ Paul Thompson III          
                                           -------------------------------------
                                           Title: Vice President


                                        PHEMUS CORPORATION


                                        By:/s/ Michael R. Eisenson          
                                           -------------------------------------
                                           Title: Authorized Signatory

                                        TENACQCO BRIDGE PARTNERSHIP
                                            By:  DLJ Capital Corporation,
                                                 as General Partner


                                        By:/s/ Paul Thompson III           
                                           -------------------------------------
                                           Title: Vice President





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                                        INTERCONTINENTAL MINING & RESOURCES 
                                          INCORPORATED


                                        By:/s/ John R. Schoemer            
                                           -------------------------------------
                                           Title: Attorney-in-Fact

                                        QUADRANT CAPITAL CORP.


                                        By:/s/ John R. Schoemer             
                                           -------------------------------------
                                           Title: Vice President



Agreed, Accepted and Acknowledged
This 17th Day of January, 1995:

SOCIETE GENERALE,
  as Agent


By:/s/ David I. Brunson        
   ----------------------------------
   Title: First Vice President





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