<PAGE>

                                                                    Exhibit 4.13


                    AMENDMENT NO. 3 TO SHAREHOLDERS AGREEMENT


         AMENDMENT NO. 3, dated as of January 1, 2001, to the Shareholders
Agreement, dated as of September 12, 1996, by and among Rayovac Corporation, a
Wisconsin corporation (the "Company") and the Shareholders of the Company
referred to therein, as amended by amendment agreements dated as of August 1,
1997 and January 8, 1997 (the "Shareholders Agreement"). Capitalized terms used
herein and not otherwise defined shall have meanings ascribed to such terms in
the Shareholders Agreement.

         WHEREAS, pursuant to Section 4.2 of the Shareholders Agreement, the
Shareholders Agreement may be amended by a written instrument duly executed by a
majority in interest of the Shareholders and, if the Lee Group Shareholders, the
Management Shareholders or the Non-Management Shareholders are adversely
affected by such amendment, by a majority in interest of each such adversely
affected group; and

         WHEREAS, the signatories hereto represent a majority in interest of the
Stockholders and a majority in interest of each of the Lee Group Shareholders
and the Management Shareholders.

         NOW THEREFORE, in consideration of the foregoing, the Shareholders
Agreement is hereby amended as follows:

         1.       The Article I definition of "Shares" shall be amended to read
                  as follows:

                  SHARES. "Shares" shall mean with respect to any Shareholder
                  (a) all shares of Common Stock held by Shareholders prior to
                  the close of trading on the New York Stock Exchange on
                  November 20, 1997, (b) all shares of Common Stock acquired in
                  one or more Permitted Transfers, (c) securities of the Company
                  issued in exchange for, upon reclassification of, or as a
                  distribution in respect of, the Common Stock referred to in
                  subs. (a) and (b) above, and (d) shares of Common Stock
                  subject to options pursuant to the Rayovac Corporation 1996
                  Stock Option Plan.

         This Amendment No. 3 may be signed in one or more counterparts, each of
which shall be deemed an original but all of which together shall constitute one
and the same instrument.


<PAGE>

AMENDMENT NO. 3 TO SHAREHOLDERS AGREEMENT


         IN WITNESS WHEREOF, the parties have executed this Amendment No. 3 to
the Shareholders Agreement as of the date first written above.

                                            RAYOVAC CORPORATION


                                            By:
                                                -------------------------------
                                                David A. Jones
                                                Chief Executive Officer


                                      -2-
<PAGE>

AMENDMENT NO. 3 TO SHAREHOLDERS AGREEMENT


LEE GROUP SHAREHOLDERS:

                                            THOMAS H. LEE EQUITY FUND III, L.P.

                                            By: THL Equity Advisors III Limited
                                                Partnership, as General Partner
                                                By: THL Equity Trust III,
                                                    as General Partner

                                            By:________________________________

                                               Name:  _________________________

                                               Title: _________________________



                                            THOMAS H. LEE FOREIGN FUND III, L.P.

                                            By: THL Equity Advisors III Limited
                                                Partnership, as General Partner
                                                By: THL Equity Trust III,
                                                    as General Partner

                                            By: _______________________________

                                                Name:  ________________________

                                                Title: ________________________



                                            THL-CCI LIMITED PARTNERSHIP

                                            By: THL Investment Management Corp.,
                                                as General Partner

                                            By: _______________________________

                                                Name:  ________________________

                                                Title: ________________________


                                      -3-
<PAGE>

AMENDMENT NO. 3 TO SHAREHOLDERS AGREEMENT


MANAGEMENT SHAREHOLDERS:



----------------------------                        ---------------------------
David A. Jones                                       Dale R. Tetzlaff



----------------------------                        ---------------------------
Luis A. Cancio                                       Randall J. Steward



----------------------------                        ---------------------------
Kenneth V. Biller                                    Kent J. Hussey



----------------------------                        ---------------------------
Merrell M. Tomlin                                    Stephen P. Shanesy


                                      -4-