<PAGE>   1

                                                                    EXHIBIT 4.16

                                SECOND AMENDMENT



                  SECOND AMENDMENT (this "Amendment"), dated as of December 18,
1997, among American Pad & Paper Company ("Holdings"), WR Acquisition, Inc. ("WR
Acquisition"), American Pad & Paper Company of Delaware, Inc. (the "Borrower"),
the lending institutions party to the Credit Agreement referred to below (each a
"Bank" and, collectively, the "Banks"), Bank of Tokyo-Mitsubishi Trust Company,
Bank One Texas, N.A., The Bank of Nova Scotia and The First National Bank of
Boston, as Co-Agents, (the "Co-Agents"), and Bankers Trust Company, as Agent
(the "Agent"). All capitalized terms used herein and not otherwise defined
herein shall have the respective meanings provided such terms in the Credit
Agreement.

                              W I T N E S S E T H :

                  WHEREAS, Holdings, WR Acquisition, the Borrower, the Banks,
the Co-Agents and the Agent are party to a Credit Agreement, dated as of July 8,
1996 (the "Credit Agreement"); and

                  WHEREAS, the Borrower has requested that the Banks provide the
amendment provided for herein and the Banks have agreed to provide such
amendment on the terms and conditions set forth herein;

                  NOW, THEREFORE, it is agreed:

                  1. Section 8.10 of the Credit Agreement is hereby amended by
inserting the following proviso at the end thereof:

                  "; provided that notwithstanding the foregoing, for the Test
                  Period ending December 31, 1997, the Borrower will not permit
                  Consolidated EBITDA to be less than $72,000,000."

                  2. Section 8.11 of the Credit Agreement is hereby amended by
inserting the following proviso at the end thereof:

                  "; provided that notwithstanding the foregoing, for the Test
                  Period ending December 31, 1997, the Borrower will not permit
                  the Interest Coverage Ratio to be less than 2.00:1.00."



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                  3. Section 8.12 of the Credit Agreement is hereby amended by
inserting the following proviso at the end thereof:

                  "; provided that notwithstanding the foregoing, for the period
                  from the Amendment Effective Date under and as defined in the
                  Second Amendment to this Agreement, dated as of December 18,
                  1997, to and including March 30, 1998, the Borrower will not
                  permit the Leverage Ratio to be more than 6.20:1.00."

                  4. In order to induce the Banks to enter into this Amendment,
each of Holdings, WR Acquisition and the Borrower hereby represents and warrants
that (i) no Default or Event of Default exists as of the Amendment Effective
Date (as defined below) after giving effect to this Amendment and (ii) on the
Amendment Effective Date, both before and after giving effect to this Amendment,
all representations and warranties contained in the Credit Agreement and in the
other Credit Documents are true and correct in all material respects.

                  5. This Amendment shall become effective on the date (the
"Amendment Effective Date") when the Required Banks, Holdings, WR Acquisition
and the Borrower shall have signed a counterpart hereof (whether the same or
different counterparts) and shall have delivered (including by way of facsimile
transmission) the same to the Agent at its Notice Office.

                  6. This Amendment is limited as specified and shall not
constitute a modification, acceptance or waiver of any other provision of the
Credit Agreement or any other Credit Document.

                  7. This Amendment may be executed in any number of
counterparts and by the different parties hereto on separate counterparts, each
of which counterparts when executed and delivered shall be an original, but all
of which shall together constitute one and the same instrument. A complete set
of counterparts shall be lodged with the Borrower and the Agent.

                  8. THIS AMENDMENT AND THE RIGHTS AND OBLIGATIONS OF THE
PARTIES HEREUNDER SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS
OF THE STATE OF NEW YORK.

                                      * * *



                                       -2-


<PAGE>   3



                  IN WITNESS WHEREOF, each of the parties hereto has caused a
counterpart of this Amendment to be duly executed and delivered as of the date
hereof.





                                        AMERICAN PAD & PAPER COMPANY



                                        By:  
                                           -----------------------------------
                                           Title:

                    
                                        WR ACQUISITION, INC.



                                        By:
                                           -----------------------------------
                                           Title:


                                        AMERICAN PAD & PAPER COMPANY
                                            OF DELAWARE, INC.



                                        By:
                                           -----------------------------------
                                           Title:


                                        BANKERS TRUST COMPANY



                                        By:
                                           -----------------------------------  
                                           Title:





<PAGE>   4



                                        ABN AMRO BANK N.V.



                                        By
                                          -----------------------------------
                                          Title:


                                        BANK LEUMI TRUST CO. OF NEW YORK



                                        By
                                          -----------------------------------   
                                          Title:


                                        THE BANK OF NEW YORK



                                        By
                                          -----------------------------------
                                          Title:


                                        THE BANK OF NOVA SCOTIA



                                        By
                                          -----------------------------------
                                          Title:





                                        BANK OF SCOTLAND



                                        By
                                          -----------------------------------
                                          Title:





<PAGE>   5



                                        BANK OF TOKYO - MITSUBISHI
                                               TRUST COMPANY



                                        By
                                          ----------------------------------- 
                                          Title:


                                        BANK ONE, TEXAS, N.A.



                                        By:
                                           -----------------------------------  
                                           Title:


                                        BANQUE PARIBAS



                                        By
                                          -----------------------------------   
                                          Title:


                                        By
                                          -----------------------------------   
                                          Title:


                                        CHRISTIANIA BANK OG
                                          KREDITKASSE, NEW YORK
                                          BRANCH



                                        By
                                          -----------------------------------
                                          Title:


                                        By
                                          -----------------------------------   
                                          Title:


                                        CIBC INC.






<PAGE>   6



                                        By
                                          -----------------------------------   
                                          Title:


                                        BANKBOSTON, N.A.



                                        By 
                                          -----------------------------------   
                                          Title:



                                        GUARANTY FEDERAL BANK,
                                         F.S.B.



                                        By
                                          -----------------------------------   
                                          Title:



                                        THE INDUSTRIAL BANK OF JAPAN,
                                        LIMITED



                                        By
                                          -----------------------------------
                                          Title:


                                        THE LONG TERM CREDIT BANK
                                            OF JAPAN, LIMITED, NEW
                                            YORK BRANCH



                                        By
                                          -----------------------------------
                                          Title:







<PAGE>   7


                                        SANWA BUSINESS CREDIT
                                            CORPORATION



                                        By
                                          -----------------------------------   
                                          Title:




                                        SOCIETE GENERALE



                                        By
                                          -----------------------------------   
                                          Title:




                                        BANK POLSKA KASA OPIEKI, S.A.



                                        By
                                          -----------------------------------
                                          Title:




                                        LEHMAN COMMERCIAL PAPER, INC.



                                        By
                                          -----------------------------------
                                          Title: