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                                                                     EXHIBIT 4.1


                                                                  EXECUTION COPY


EXECUTION COPY

                               TELECORP PCS, INC.


                                  $171,274,000

                 11% Senior Subordinated Discount Notes due 2011

                               FIRST AMENDMENT TO

                   EXCHANGE AND REGISTRATION RIGHTS AGREEMENT

                                  June 4, 2001

Lucent Technologies Inc.
600 Mountain Avenue
Murray Hill, New Jersey 07974

Ladies and Gentlemen:

     TeleCorp PCS, Inc. (formerly known as TeleCorp-Tritel Holding Company), a
Delaware corporation (the "Company"), and you (the "Purchaser"), currently the
holder of all of the Securities (as defined herein), are parties to (a) that
certain Securities Purchase Agreement dated as of April 3, 2001 (the "Purchase
Agreement"), pursuant to which you purchased from the Company on April 6, 2001
$171,274,000 aggregate principal amount at maturity of the Company's 11% Senior
Subordinated Discount Notes due April 15, 2011 (the "Securities") and (b) that
certain Exchange and Registration Rights Agreement dated as of April 6, 2001
(the "Registration Rights Agreement"). Capitalized terms used but not defined
herein shall have the meanings given to such terms in the Registration Rights
Agreement.

     In accordance with Section 10(a) thereof, the Company and the Purchaser
hereby amend the Registration Rights Agreement as follows:

     1. The first paragraph of Section 1 of the Registration Rights Agreement,
captioned "Registered Exchange Offer," shall be amended and restated to read in
its entirety as follows:


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         "1. Registered Exchange Offer. The Company shall (i)(A) prepare and (B)
not later than 60 days (or, if the Issue Date (as defined herein) shall fall in
January 2002, such number of days, not less than 60, as shall equal the number
of days between the Issue Date and the third business day following the day on
which the Company files with the Commission its Annual Report on Form 10-K with
respect to its preceding fiscal year) following the date on which the Purchaser
gives written notice to the Company to commence a registration pursuant to the
Securities Act as contemplated by this Agreement (the date on which such notice
is given, the "Issue Date"), file with the Commission a registration statement
(the "Exchange Offer Registration Statement") on an appropriate form under the
Securities Act with respect to a proposed offer to the Holders of the Securities
(the "Registered Exchange Offer") who are not prohibited by applicable law or
interpretations thereof by the Commission's staff from participating in the
Registered Exchange Offer to issue and deliver to such Holders, in exchange for
the Securities, a like aggregate principal amount of debt securities of the
Company (the "Exchange Securities") that are identical in all material respects
to the Securities, except for the transfer restrictions and registration rights
relating to the Securities, (ii) use its commercially reasonable efforts to
cause the Exchange Offer Registration Statement to become effective under the
Securities Act no later than 180 days after the Issue Date and the Registered
Exchange Offer to be consummated no later than 210 days after the Issue Date and
(iii) keep the Exchange Offer Registration Statement effective for not less than
30 days (or longer, if required by applicable law) after the date on which
notice of the Registered Exchange Offer is mailed to the Holders (such period
being called the "Exchange Offer Registration Period"); provided that the
Company may elect to close the Registered Exchange Offer 30 days after the
commencement thereof (unless otherwise required by applicable law), so long as
the Company has accepted all Securities validly tendered in accordance with the
terms of the Registered Exchange Offer. Notwithstanding the preceding sentence,
the Issue Date must occur on or prior to October 9, 2002 , the 180th day
preceding the second anniversary of the date on which the Securities were
originally issued. The Exchange Securities will be issued under the Indenture or
an indenture (the "Exchange Securities Indenture") between the Company and the
Trustee or such other bank or trust company that is reasonably satisfactory to
the Purchasers, as trustee (the "Exchange Securities Trustee"), such indenture
to be identical in all material respects to the Indenture, except for the
transfer restrictions and registration rights relating to the Securities (as
described above)."

         2. The last clause of the third to last paragraph of Section 1 of the
Registration Rights Agreement shall be amended and restated to read in its
entirety as follows: "from April 6, 2001."

         3. The parenthetical in the second and third lines of subsection (a) of
Section 2 of the Registration Rights Agreement, captioned "Shelf Registration,"
shall be amended and restated to read in its entirety as follows: "(but in no
event more than 60 days after so required or requested pursuant to this Section
2, subject to the parenthetical in the first sentence of Section 1 hereof)".

         4. The first sentence of subsection (b) of Section 2 of the
Registration Rights Agreement, captioned "Shelf Registration," shall be amended
and restated to read in its entirety as follows:

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         "(b) the Company shall use its commercially reasonable efforts to keep
the Shelf Registration Statement continuously effective in order to permit the
prospectus forming part thereof to be used by Holders of Transfer Restricted
Securities for a period ending on the earlier of (i) April 6, 2003 or such
earlier date when all the Transfer Restricted Securities covered by the Shelf
Registration Statement have been sold pursuant thereto and (ii) the date on
which the Securities become eligible for resale without volume restrictions
pursuant to Rule 144 under the Securities Act (in any such case, such period
being called the "Shelf Registration Period")."

         5. Subsection (a)(i) of Section 3 of the Registration Rights Agreement,
captioned "Liquidated Damages," is hereby amended and restated in its entirety
to read as follows: "(i) the applicable Registration Statement is not filed with
the Commission on or prior to 60 days after the Issue Date (subject to the
parenthetical in the first sentence of Section 1 hereof),".

         6. The parenthetical in subsection (a)(ii), and the first parenthetical
in subsection (a)(iv), of Section 3 of the Registration Rights Agreement,
captioned "Liquidated Damages," are hereby amended and restated to read, each in
its entirety as follows: "(or in the case of a Shelf Registration Statement
required to be filed in response to a change in applicable law or
interpretations thereof by the Commission's staff, if later, within 60 days
after publication of the change in law or interpretation, subject to the
parenthetical in the first sentence of Section 1 hereof)".

         7. Except as amended hereby, the Registration Rights Agreement shall
remain in full force and effect in accordance with its original terms.

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         Please confirm that the foregoing correctly sets forth the agreement
between the Company and the Purchaser.




                                       Very truly yours,



                                       TELECORP PCS, INC.



                                       By: /s/ Thomas H. Sullivan
                                           ---------------------------
                                       Name:  Thomas H. Sullivan
                                       Title: Executive Vice President
                                              and Chief Financial Officer

Accepted:
LUCENT TECHNOLOGIES INC.



By: /s/James Lewis
   -----------------------------------
    Name:  James Lewis
    Title:  Director Customer Finance


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