<PAGE>
 
                                                                   Exhibit 10.35

                             AMENDED AND RESTATED
                             SUCCESS FEE AGREEMENT
                             ---------------------

     This SUCCESS FEE AGREEMENT, made as of February 23, 1999 (this
"Agreement"), by and between Little Switzerland, Inc., a Delaware corporation
with its main office in St. Thomas, U.S.V.I. (the "Company"), and C. William
Carey ("CWC").

                                  WITNESSETH

     WHEREAS, the parties hereto entered into a Success Fee Agreement on 
January 15, 1999 (the "Original Agreement"), relating to a success fee for
certain transactions entered into and completed by the Company;

     WHEREAS, CWC has informed the Company that he will not stand for re-
election as a director of the Company at the Company's 1998 Annual Meeting of
Stockholders;

     WHEREAS, CWC has agreed to resign as the Acting Chief Executive Officer and
President of the Company effective as of the close of business on April 7, 1999;
and

     WHEREAS, the parties hereto now desire to amend and restate the Original
Agreement.

     NOW, THEREFORE, in consideration of the foregoing premises and the mutual
covenants contained herein, the Company and CWC mutually agree as follows:

     1.     Payment of Success Fee.  CWC hereby agrees that, if requested in
            ----------------------                                          
writing by the Board of Directors of the Company, he shall actively participate,
through duties and responsibilities assigned to CWC by the Board of Directors of
the Company, in the negotiation, structuring and/or closing of a transaction or
a series of related transactions, if any, approved by the Board of Directors of
the Company which are a tender or exchange offer, merger, reorganization,
consolidation or other business combination that directly result in the sale or
other disposition of all or substantially all of the assets of the Company or a
sale of all or substantially all of the issued and outstanding stock of the
Company (a "Transaction").  If the Board of Directors of the Company requests in
writing that CWC participate in the Transaction and subject to Section 3 hereof,
for compensation for all of such services rendered by CWC in connection with
such Transaction, the Company shall pay CWC an amount equal to eighty three and
one-third percent (83 1/3%) of two-thirds of one percent (1%) of the Aggregate
Value (as defined in Section 2 hereof) of the Transaction (the "Success Fee") by
wire transfer of immediately available funds to an account designated by CWC on
the closing date (the "Effective Time") of such Transaction.

     2.     Aggregate Value.  For purposes of this Agreement, the term
            ---------------                                           
"Aggregate Value" shall mean the total amount of cash and the fair market value
(on the date of payment) of all other property paid or payable, directly or
indirectly, by the acquiring party (the "Acquiror") to the acquired party or the
seller of the acquired business (the "Acquired"), or to the Acquired's security
<PAGE>
 
holders or its employees, or by the Acquired to the Acquired's security holders,
in connection with a Transaction (including, without limitation, amounts paid by
the Acquiror to holders of any warrants, stock purchase rights, convertible
securities or similar rights of the Company and to holders of any options or
stock appreciation rights issued by the Company, whether or not vested).
Aggregate Value shall also include the value of any long-term liabilities
(including the short-term portion thereof) of the Company (including the
principal amount of any indebtedness for borrowed money) indirectly or directly
assumed or acquired by the Acquiror, or otherwise repaid or retired, in
connection with or in anticipation of a Transaction.  In the event the
Transaction takes the form of a recapitalization or restructuring of the Company
(including, without limitation, through negotiated repurchases of its
securities, an issuer tender offer, an extraordinary dividend, a spin-off,
split-off or similar transaction), Aggregate Value shall also include the fair
market value of (i) the equity securities of the Company retained by the
Company's security holders following such Transaction and (ii) any cash,
securities (including securities of subsidiaries) or other consideration
received by the Company's security holders in exchange for or in respect of
securities of the Company in connection with such Transaction (all such cash,
securities or other consideration received by such security holders being deemed
to have been paid to such security holders in such Transaction).  If a
Transaction takes the form of a sale of assets, Aggregate Value shall also
include (i) the value of any current assets not sold, minus (ii) the value of
any current liabilities not assumed by the Acquiror.  In the event that any part
of the consideration in connection with a transaction will be payable (whether
in one payment or a series of two or more payments) at any time following the
consummation thereof, the term Aggregate Value shall include the present value
of such future payment of payments.  As used in this Agreement, the terms
"payment," "paid" or "payable" shall be deemed to include, as applicable, the
issuance or delivery of securities or other property other than cash.

     3.     Director Sponsored Transaction.  Notwithstanding anything to the
            ------------------------------                                  
contrary contained herein, the Company shall not be obligated to pay the Success
Fee to CWC if the Transaction involves any person, company or entity (i) that is
operated by CWC, (ii) for which CWC is performing or has performed, in the
twelve (12) months preceding the execution of the definitive documents relating
to the Transaction, any material advisory or consulting services, (iii) that
employs CWC or (iv) in which CWC owns or has an agreement to own more than an
one percent (1%) equity interest in a privately-held corporation or a five
percent (5%) equity interest in a publicly-held corporation.

     4.     Satisfaction of the Company's Obligations; Interest.  The Company
            ---------------------------------------------------              
and CWC agree that the payment provided for in Section 1 hereof shall satisfy in
full the Company's obligation to pay the Success Fee to CWC with respect to the
services rendered by CWC in connection with this Agreement. Notwithstanding the
foregoing, in the event that the Company shall fail to pay the Success Fee when
due, the term "Success Fee" shall be deemed to include interest on such unpaid
Success Fee, commencing on the Effective Time, at a rate per annum equal to the
rate of interest publicly announced by Citibank, N.A., from time to time, in the
City of New York, as such bank's Prime Rate.

     5.     Legal Fees.  If legal action is commenced by either party hereto to
            ----------                                                         
enforce his or its respective rights under this Agreement and a court of
competent jurisdiction enters a judgment for such party, then the prevailing
party shall be entitled to recover any and all costs incurred in connection with
the enforcement of his or its, as the case may be, rights hereunder, including,
without limitation, reasonable attorney's fees, in addition to any other relief
granted.

                                       2
<PAGE>
 
     6.     Arbitration of  Disputes.  Any controversy or claim arising out of
            ------------------------                                          
or relating to this Agreement or the breach thereof shall, to the fullest extent
permitted by law, be settled by arbitration in any forum and form agreed upon by
the parties or, in the absence of such an agreement, under the auspices of the
American Arbitration Association ("AAA") in Boston, Massachusetts in accordance
with the rules of the AAA, including, but not limited to, the rules and
procedures applicable to the selection of arbitrators.  Judgment upon the award
rendered by the arbitrator may be entered in any court having jurisdiction
thereof. This Section 6 shall be specifically enforceable. Notwithstanding the
foregoing, this Section 6 shall not preclude either party from pursuing a court
action for the sole purpose of obtaining a temporary restraining order or a
preliminary injunction in circumstances in which such relief is appropriate;
provided, however, that any other relief shall be pursued through an arbitration
proceeding pursuant to this Section 6.

     7.     Binding Effect; Assignment.  This Agreement shall inure to the
            --------------------------                                    
benefit of and be binding upon the Company and CWC, their respective successors,
executors, administrators, heirs and permitted assigns.  CWC shall have no right
to assign this Agreement.  The Company may assign this Agreement only with the
consent of CWC.

     8.     Amendment.  This Agreement may be amended or modified only by a
            ---------                                                      
written instrument signed by CWC or a duly authorized representative of CWC and
the Company.

     9.     Termination.  If the Effective Time has not occurred by January 15,
            -----------                                                        
2000 (the "Termination Date"), regardless of the reason therefor, then this
Agreement shall automatically terminate on such Termination Date and all of the
Company's obligations hereunder shall cease as of such Termination Date.

     10.    Counterparts.  This Agreement may be executed in one or more
            ------------                                                
counterparts, all of which documents shall be considered one and the same
document.

     11.    Governing Law; Consent to Jurisdiction.  It is the parties'
            --------------------------------------                     
intention that this Agreement shall be construed under and be governed in all
respects by the laws of the State of Delaware.  Each of the Company and CWC
hereby irrevocably and unconditionally consent to the sole and exclusive
jurisdiction of the courts of the State of Delaware and the United States
District Court for the District of Delaware for any action, suit or proceeding
arising out of or relating to this Agreement, and agrees not to commence any
action, suit or proceeding related thereto except in such courts.  Each of the
Company and CWC further hereby irrevocably and unconditionally waive any
objection to the laying of venue of any lawsuit, claim or other proceeding
arising out of or relating to this Agreement in the courts of the State of
Delaware or the United States District Court for the District of Delaware, and
hereby further irrevocably and unconditionally waive and agree not to plead or
claim in any such court that any such lawsuit, claim or other proceeding brought
in any such court has been brought in an inconvenient forum.

                                       3
<PAGE>
 
     12.    Effectiveness.  The effectiveness of this Agreement is contingent on
            -------------                                                       
the election of Adriane J. Dudley, Seymour Holtzman, Melanie Sturm and Richard
C. Hunter, the Board of Directors' nominees for directors of the Company, at the
Company's 1998 Annual Meeting of Stockholders, as set forth in a settlement
agreement, dated as of the date hereof, entered into by the Company, CWC and the
other parties identified therein.  In the event such election does not occur,
this Agreement shall forthwith become null and void and have no effect, without
any liability on the part of any party hereto.

     13.    Severability.   In case provisions of this Agreement shall be
            ------------                                                 
invalid, illegal or unenforceable, the validity, legality and enforceability of
the remaining provisions of this Agreement shall not in any way be affected or
impaired thereby.

     14.    Entire Agreement.  This Agreement is the entire agreement between
            ----------------                                                 
CWC and the Company, and all previous agreements, or promises between CWC and
the Company relating to the subject matter of this Agreement are superseded,
null, and void. Notwithstanding the foregoing, the parties hereto acknowledge
that they are simultaneously herewith entering into or are parties to a
Consulting Agreement, a Severance Agreement and a Settlement Agreement.

                                 [END OF TEXT]

                                       4
<PAGE>
 
     IN WITNESS WHEREOF, this Agreement has been executed by the Company, by its
duly authorized directors, and by CWC, as of the date first above written.

 
                                 LITTLE SWITZERLAND, INC.



                                 By: /s/ Adriane J. Dudley
                                     -----------------------
                                     Name: Adriane J. Dudley
                                     Title: Director
 

                                 CWC:
 

                                 /s/ C. William Carey
                                 ---------------------------
                                 C. William Carey

                                       5