<PAGE>

                                                                   EXHIBIT 4.1.2

                                    AMENDMENT
                            TO STOCKHOLDERS AGREEMENT
                          Dated as of January 29, 2001


     DDi Corp., a Delaware corporation (the "Company"), Bain Capital Fund V,
L.P., Bain Capital Fund V-B, L.P., BCIP Associates, L.P., and BCIP Trust
Associates, L.P., and the other signatories hereto:

      1.    Reference to the Stockholders Agreement; Definitions. Reference is
            made to the Stockholders Agreement dated as of March 31, 2000 (as
            amended, the "Stockholders Agreement"), among the Company and the
            holders of its equity interests (including without limitation the
            other parties hereto). Terms defined in the Stockholders Agreement
            and not otherwise defined herein are used herein with the meanings
            so defined.

      2.    Amendment. Pursuant to Section 12.2 of the Stockholders Agreement,
            each Investor (constituting the Majority Investors) and each other
            signatory hereto hereby agrees to amend Section 8.3.1.1 of the
            Stockholders Agreement by deleting the phrase "20 days after the
            effectiveness" therein and replacing it with the phrase "8 days
            after the mailing by the Company by registered mail or overnight
            delivery".

      3.    Miscellaneous. Except to the extent specifically amended hereby, the
            provisions of the Stockholders Agreement shall remain unmodified,
            and, subject to the conditions contained in this Amendment, the
            Stockholders Agreement is hereby confirmed as being in full force
            and effect. This Amendment may be executed in any number of
            counterparts which together shall constitute one instrument, shall
            be governed by and construed in accordance with the laws of the
            State of Delaware, without regard to the conflict of laws rules of
            any jurisdictions.
<PAGE>

                                                                    Amendment to
                                                          Stockholders Agreement
                                                                January 29, 2001


      In WITNESS WHEREOF, the parties have caused this Amendment to the
Stockholders Agreement to be executed and delivered as of the date first above
written.


                            DDI CORP.



                            By________________________________
                              Name:
                              Title:

INVESTORS:
                            BAIN CAPITAL FUND V, L.P.
                            BAIN CAPITAL FUND V-B, L.P.

                            By Bain Capital Partners V, L.P.,
                                   their general partner

                               By Bain Capital Investors V, Inc.,
                                 its general partner


                               By_____________________________
                                 Name:
                                 Title:  Managing Director


                            BCIP ASSOCIATES
                            BCIP TRUST ASSOCIATES, L.P.


                            By___________________________________
                              Name:
                              Title: a general partner



                                       2
<PAGE>

                                                                    Amendment to
                                                          Stockholders Agreement
                                                                January 29, 2001

OTHER INVESTORS:
                            CELERITY DYNAMO, L.L.C.


                            By________________________________
                               its

                            CELERITY LIQUIDS, L.L.C.


                            By_______________________________
                               its

                            CELERITY DETAILS, L.L.C.


                            By________________________________
                               its


                                       3
<PAGE>

                                                                    Amendment to
                                                          Stockholders Agreement
                                                                January 29, 2001

MANAGERS:


                            _________________________________
                            Charles D. Dimick


                            _________________________________
                            Bruce D. McMaster


                            _________________________________
                            Joseph P. Gisch




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