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                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                  SCHEDULE 14A

          Proxy Statement Pursuant to Section 14(a) of the Securities
                     Exchange Act of 1934 (Amendment No.  )

Filed by the Registrant [X]
Filed by a Party other than the Registrant [ ]

Check the appropriate box:

[ ]  Preliminary Proxy Statement.
[ ]  CONFIDENTIAL, FOR USE OF THE COMMISSION ONLY (AS PERMITTED BY
     RULE 14a-6(e)(2)).
[ ]  Definitive Proxy Statement.
[X]  Definitive Additional Materials.
[ ]  Soliciting Material Pursuant to Section 240.14a-12


                        WALLACE COMPUTER SERVICES, INC.
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                (Name of Registrant as Specified In Its Charter)


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    (Name of Person(s) Filing Proxy Statement, if other than the Registrant)

Payment of Filing Fee (check the appropriate box):

[X]  No fee required.

[ ]  Fee computed on table below per Exchange Act Rules 14a-6(i)(1) and 0-11.

     1) Title of each class of securities to which transaction applies:

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

     2) Aggregate number of securities to which transaction applies:

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

     3) Per unit price or other underlying value of transaction computed
        pursuant to Exchange Act Rule 0-11 (set forth the amount on which the
        filing fee is calculated and state how it was determined):

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

     4) Proposed maximum aggregate value of transaction:

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

     5) Total fee paid:

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

[ ]  Fee paid previously with preliminary materials.

[ ]  Check box if any part of the fee is offset as provided by Exchange Act
     Rule 0-11(a)(2) and identify the filing for which the offsetting fee was
     paid previously. Identify the previous filing by registration statement
     number, or the Form or Schedule and the date of its filing.

     1) Amount Previously Paid:

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

     2) Form, Schedule or Registration Statement No.:

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

     3) Filing Party:

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     4) Date Filed:

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PERSONS WHO POTENTIALLY ARE TO RESPOND TO THE COLLECTION OF INFORMATION
CONTAINED IN THIS FORM ARE NOT REQUIRED TO RESPOND UNLESS THE FORM DISPLAYS A
CURRENTLY VALID OMB CONTROL NUMBER.

SEC 1913 (02-02)


                                 UPDATED NOTICE
            IMPORTANT NOTICE TO DIRECTORS AND EXECUTIVE OFFICERS OF
                        WALLACE COMPUTER SERVICES, INC.
                    CONCERNING THE BLACKOUT PERIOD UNDER THE
                 THE WALLACE PROFIT SHARING AND RETIREMENT PLAN
     AND THE WALLACE COMMERCIAL PRINT 401(k) RETIREMENT PLAN (THE "PLANS")


                                 APRIL 16, 2003


     1. This notice is being provided to you to inform you that in connection
with the proposed merger of Wallace Computer Services, Inc. ("Wallace") with a
wholly owned subsidiary of Moore Corporation Limited ("Moore"), as a result of
which Wallace will become a wholly owned subsidiary of Moore (the "Merger"),
each of the Wallace Stock Funds under the Wallace Profit Sharing and Retirement
Plan and the Wallace Commercial Print 401(k) Retirement Plan (the "Plans") will
be converted into a stock fund primarily holding Moore common shares (the "Moore
Wallace Stock Fund") as soon as administratively practicable after the effective
time of the consummation of the Merger (the "Effective Time"). THIS UPDATED
NOTICE IS BEING PROVIDED TO YOU ONLY TO INFORM YOU THAT THE DATES UPON WHICH THE
BLACKOUT PERIOD IS EXPECTED TO BEGIN AND END HAVE BEEN CHANGED AND IS OTHERWISE
IDENTICAL TO THE PREVIOUS NOTICE YOU RECEIVED DATED APRIL 11, 2003.

     2. In connection with this proposed Merger, participants in the Plans will
be temporarily unable to transfer any portion of their account balances either
into or out of the Wallace Stock Fund. Moreover, participants with all or a
portion of their account balances invested in the Wallace Stock Fund will be
temporarily unable to receive a distribution of all or such portion of their
account balance. Finally, participants who have elected to have all or a portion
of their contributions under the Plans invested in the Wallace Stock Fund will
be temporarily suspended from investing new contributions in the Wallace Stock
Fund. This period during which participants will temporarily be unable to
exercise these rights otherwise available to them under the Plans is called a
"blackout period."

     3. The blackout period for the Plans is expected to begin during the
week of May 11, 2003 and is expected to end the week of May 25, 2003. PLEASE
NOTE THAT THESE DATES HAVE CHANGED SINCE THE NOTICE DATED APRIL 11, 2003 WAS
PREVIOUSLY PROVIDED TO YOU. THESE DATES HAVE BEEN ADJUSTED TO REFLECT THE
EXPECTED DATE OF THE EFFECTIVE TIME. During these weeks, you can determine
whether the blackout period has started or ended by calling Lewis Jacobson or
Chris Gicela of the Wallace Retirement Plans department toll-free at
1-877-799-9350.

     4. Pursuant to Section 306(a) of the Sarbanes-Oxley Act of 2002, as a
director or executive officer of Wallace, during this blackout period you will
not be permitted to purchase, sell or otherwise acquire or transfer, directly or
indirectly, any Wallace common shares to the extent such shares are, or were,
acquired in connection with your service or employment as a director or
executive officer of Wallace (including, but not limited to, any Wallace common
shares you hold in order to comply with share ownership guidelines). Moreover,
if you are or become a director or executive officer of Moore after the
Effective Time, for the duration of the blackout period you will similarly be
prohibited from purchasing, selling or otherwise acquiring or transferring,
directly or indirectly, any Moore common shares which you receive in respect of
Wallace common shares acquired in connection with your service or employment as
a director or executive officer of Wallace. While the receipt of Moore common
shares in exchange for Wallace common shares in connection with the Merger is
exempt from this prohibition, if you are contemplating any other transactions
involving Wallace common shares or Moore common shares, please contact James D.
Benak, General Counsel, Wallace Computer Services, Inc. 2275 Cabot Drive, Lisle,
IL, 60532-3630, (630) 588-6475 for more information on whether such shares are,
or were, "acquired in connection with your service or employment as a director
or executive officer of Wallace."

     5. If you have any other questions concerning this notice or whether
certain transactions are subject to this prohibition, you should contact James
D. Benak, General Counsel, Wallace Computer Services, Inc. 2275 Cabot Drive,
Lisle, IL, 60532-3630, (630) 588-6475.


 THIS RELEASE MAY BE DEEMED TO BE SOLICITATION MATERIAL IN RESPECT OF WALLACE'S
  PROPOSED MERGER WITH A WHOLLY-OWNED SUBSIDIARY OF MOORE. ON APRIL 14, 2003,
 MOORE FILED AN AMENDED REGISTRATION STATEMENT ON FORM S-4 WITH THE SECURITIES
    AND EXCHANGE COMMISSION CONTAINING A PROXY STATEMENT/PROSPECTUS. WALLACE
 COMMENCED MAILING THE PROXY STATEMENT/PROSPECTUS TO WALLACE SECURITYHOLDERS ON
  OR ABOUT APRIL 15, 2003. INVESTORS AND SECURITYHOLDERS ARE URGED TO READ THE
 REGISTRATION STATEMENT, THE PROXY STATEMENT/PROSPECTUS AND ANY OTHER RELEVANT
 DOCUMENTS FILED OR THAT WILL BE FILED WITH THE SEC WHEN THEY BECOME AVAILABLE
 BECAUSE THEY WILL CONTAIN IMPORTANT INFORMATION. INVESTORS AND SECURITYHOLDERS
WILL BE ABLE TO RECEIVE THE PROXY STATEMENT/PROSPECTUS AND OTHER DOCUMENTS FREE
  OF CHARGE AT THE SEC'S WEB SITE, WWW.SEC.GOV., MOORE SECURITYHOLDERS WILL BE
  ABLE TO RECEIVE THE DEFINITIVE VERSION OF THE PROXY STATEMENT/PROSPECTUS AND
    OTHER DOCUMENTS FREE OF CHARGE FROM MOORE CORPORATION LIMITED, C/O MOORE
EXECUTIVE OFFICES, ONE CANTERBURY GREEN, STAMFORD, CONNECTICUT 06901, ATTENTION:
    INVESTOR RELATIONS, TEL. (203) 406-3700 OR AT WWW.MOORE.COM, AND WALLACE
  SECURITYHOLDERS WILL BE ABLE TO RECEIVE THE DEFINITIVE VERSION OF THE PROXY
STATEMENT/PROSPECTUS AND OTHER DOCUMENTS FREE OF CHARGE FROM INVESTOR RELATIONS,
    WALLACE COMPUTER SERVICES, INC., 2275 CABOT DRIVE, LISLE, IL 60532-3630,
 TEL. (630) 588-5000 OR AT WWW.WALLACE.COM. MOORE, WALLACE AND THEIR RESPECTIVE
 DIRECTORS AND EXECUTIVE OFFICERS AND OTHER MEMBERS OF MANAGEMENT AND EMPLOYEES
 MAY BE DEEMED TO BE PARTICIPANTS IN THE SOLICITATION OF PROXIES IN RESPECT OF
THE PROPOSED TRANSACTION. INFORMATION ABOUT THE DIRECTORS AND EXECUTIVE OFFICERS
OF MOORE AND THEIR OWNERSHIP OF MOORE SHARES IS SET FORTH IN THE PROXY STATEMENT
   FOR MOORE'S 2003 ANNUAL MEETING OF SHAREHOLDERS. INFORMATION REGARDING THE
 INTERESTS OF WALLACE'S DIRECTORS AND EXECUTIVE OFFICERS IN THE PROPOSED MERGER
   IS SET FORTH IN THE PROXY STATEMENT/PROSPECTUS, FILED ON APRIL 14, 2003 BY
         MOORE, THAT  WAS FIRST MAILED TO WALLACE SECURITYHOLDERS ON OR
                             ABOUT APRIL 15, 2003.