Exhibit 10.4
                                                                    ------------


                               AMENDMENT NO. 1 TO
                        INVESTORS STOCKHOLDERS' AGREEMENT

         AMENDMENT  NO.  1.  ("Amendment  No.  1")  to  Inwestors  Stockholders'
Agreement  (as  defined  below)  dated as of  September  4,  2001,  by and among
TeleCorp PCS, Inc. (the "Company") and the Cash Equity  Investors (as defined in
the Investors  Stockholders'  Agreement)  signatory hereto. Any capitalized term
used herein and not otherwise  defined  shall have the meaning  ascribed to such
term in the Investors Stockholders' Agreement.

         WHEREAS,  each of the  parties  hereto  (other  than the  Company)  are
stockholders of the Company;

         WHEREAS,  the  parties  hereto are  parties to that  certain  Investors
Stockholders' Agreement,  dated as of February 28, 2000 with respect to the Cash
Equity Investors  signatory  thereto and as of November 13, 2000 with respect to
the Company (the "Investors Stockholders' Agreement"),  pursuant to which, among
other things, the parties hereto entered into certain  agreements  regarding the
management of the Company;

         WHEREAS,  the parties hereto desire to amend certain  provisions of the
Investors Stockholders' Agreement;

         NOW,  THEREFORE,  in consideration of the mutual promises and covenants
herein contained and for other good and valuable  consideration  the receipt and
sufficiency  of  which is  hereby  acknowledged,  the  parties  hereby  agree as
follows:

         1.  Amendments.  From and after the  Amendment  Effectiveness  Date (as
hereinafter defined):

               a.   Section 2(a)(iii) of the Investors  Stockholders'  Agreement
                    shall be amended by deleting the following:

          "Dresdner (or its Affiliated  Successors)  and shall initially be Alex
          Coleman (the "Dresdner Designee")"

               and replacing it with the following:

          "CTIHC,   Incorporated  (or  its  Affiliated   Successors)  and  shall
          initially be Gary Wendt".

         2.  Amendment  Effectiveness  Date.  This  Amendment  No.  1  shall  be
effective  on the date that a  counterpart  hereof  shall have been  executed in
accordance  with Section  5.1(b) of the Investors  Stockholders'  Agreement (the
"Amendment Effectiveness Date").

         3.  Severability  of Provisions.  Any provision of this Amendment No. 1
which is prohibited  or  unenforceable  in any  jurisdiction  shall,  as to such
jurisdiction,   be   ineffective   to  the   extent  of  such   prohibition   or
unenforceability without invalidating the

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remaining  provisions  hereof or affecting the validity of remaining  provisions
hereof or affecting  the  validity or  enforceability  of such  provision in any
other jurisdiction.

         4. Agreements to Remain in Full Force and Effect.  This Amendment No. 1
shall be deemed to be an amendment to the Investors Stockholders' Agreement. All
references to the Investors  Stockholders'  Agreement in any other agreements or
documents shall on and after the date hereof be deemed to refer to the Investors
Stockholders'  Agreement  as  amended  hereby.  Except as  amended  hereby,  the
Investors  Stockholders'  Agreement shall remain in full force and effect and is
hereby ratified, adopted and confirmed in all respects.

         5.  Headings.  The headings in this  Amendment  No. 1 are inserted for
convenience and identification only and are not intended to describe, interpret,
define or limit the  scope,  extent  or  intent of this  Amendment  No. 1 or any
provision thereof.

         6. Counterparts.  This Amendment No. 1 may be executed in counterparts,
each of which  shall be  deemed an  original,  but all of which  together  shall
constitute one and the same instrument.

         7.  Governing Law. THIS AMENDMENT NO. 1 SHALL BE GOVERNED AND CONSTRUED
IN ACCORDANCE WITH THE INTERNAL LAWS OF THE STATE OF DELAWARE.

                            [SIGNATURE PAGES FOLLOW]



<PAGE>

         IN WITNESS  WHEREOF, each of the parties has executed or consent this
Amendment No. 1 to be executed by its duly authorized officers as of the date
first written above.


                                       TELECORP PCS, INC.
                                       (f/k/a TeleCorp-Tritel Holding Company)

                                       By:  /s/ Thomas H. Sullivan
                                           ------------------------------------
                                           Name:
                                           Title:

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                                      EQUITY-LINKED INVESTORS-II

                                      By: Rohit M. Desai Associates-II,
                                          its general partner

                                      By:  /s/ Frank J. Pados
                                          --------------------------------------
                                          Name:
                                          Title:


                                      PRIVATE EQUITY INVESTORS III, L.P.

                                      By: Rohit M. Desai Associates III, LLC,
                                          its general partner

                                      By:  /s/ Frank J. Pados
                                          --------------------------------------
                                          Name:
                                          Title:



<PAGE>


                                       WHITNEY EQUITY PARTNERS, L.P.

                                       By: J.H. Whitney Equity Partners, L.L.C.,
                                           its general partner

                                       By:  /s/ Daniel J. O'Brien
                                           ------------------------------------
                                           Name:  Daniel J. O'Brien
                                           Title: Managing Member of General
                                                  Partner


                                       J.H. WHITNEY III, L.P.

                                       By: J.H. Whitney Equity Partners III,
                                           L.L.C., its general partner

                                       By:  /s/ Daniel J. O'Brien
                                           ------------------------------------
                                           Name:  Daniel J. O'Brien
                                           Title: Managing Member


                                       WHITNEY STRATEGIC PARTNERS III, L.P.

                                       By: J.H. Whitney Equity Partners III,
                                           L.L.C., its general partner

                                       By:  /s/ Daniel J. O'Brien
                                           ------------------------------------
                                           Name:  Daniel J. O'Brien
                                           Title: Managing Member


<PAGE>


                                       CTIHC, INCORPORATED

                                       By:  /s/ William T. Devanney
                                           -------------------------------------
                                           Name:  William T. Devanney
                                           Title: SVP


<PAGE>

                                       CB CAPITAL INVESTORS, L.P.

                                       By: CB Capital Investors, Inc.,
                                           its general partner

                                       By:  /s/ Michael R. Hannan
                                           ------------------------------------
                                           Name:  Michael R. Hannan
                                           Title: General Partner/Managing
                                                  Director, JP Morgan Partners


<PAGE>

                                       HOAK COMMUNICATIONS PARTNERS, L.P.

                                       By: HCP Investments, L.P.,
                                           its general partner

                                       By: Hoak Partners, LLC,
                                           its general partner

                                       By:  /s/ James M. Hoak
                                           ------------------------------------
                                           Name:
                                           Title:


                                       HCP CAPITAL FUND, L.P.

                                       By: James M. Hoak & Co.,
                                           its general partner

                                       By:  /s/ James M. Hoak
                                           ------------------------------------
                                           Name:
                                           Title: