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                                                                   EXHIBIT 10.31



                 FIRST AMENDMENT TO LICENSE PURCHASE AGREEMENT

               This First Amendment to License Purchase Agreement (the "First
Amendment") is made the 17th day of December, 1999 by and between Cricket
Holdings, Inc., a Delaware Corporation (the "Buyer") and Airgate Wireless,
L.L.C., a Delaware limited liability company (the "Seller") with respect to that
certain License Purchase Agreement, dated as of September 11, 1998, by and
between Buyer and Seller (the "License Purchase Agreement"). Unless defined
herein capitalized terms shall have the meanings set forth in the License
Purchase Agreement.

               WHEREAS, Leap Wireless International, Inc. ("Leap"), the original
"Buyer" under the License Purchase Agreement, has assigned all if its rights
thereunder to Cricket Holdings, Inc., a wholly owned subsidiary of Leap pursuant
to Section 10(d) of the License Purchase Agreement and Buyer has assumed all of
Leap's obligations thereunder.

               WHEREAS, the term of the License Purchase Agreement has expired,
and Seller and Buyer would like to extend the term of the License Purchase
Agreement;

               WHEREAS, on July 22, Leap was granted Designated Entity status by
the FCC ("DE Status") which DE Status is currently subject to a motion for
reconsideration by a third party;

               WHEREAS, Buyer and Seller desire to the amend the terms of the
License Purchase Agreement pursuant to the terms set forth herein;

               NOW, THEREFORE, in consideration of the mutual covenants
contained herein, and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto, each intending
to be legally bound, do hereby agree as follows:

1. RELEASE OF FUNDS. Upon execution of this Amendment, Buyer will deliver a
letter to the Escrow Agent instructing the Escrow Agent to immediately release
the Initial Payment to Seller.

2. INCREASE THE PURCHASE PRICE. Section 1(b) is hereby amended to increase the
purchase price to twenty five million dollars ($25,000,000).

3. AMENDMENT TO CLOSING. Section 2(a) and (b) of the License Purchase Agreement
is hereby deleted and in lieu thereof the following is inserted:

        "Closing Date. The Closing shall take place within seven (7) business
        days after the waiting period applicable under the Hart Scott Rodino
        Antitrust Improvements Act ("HSR") has expired or has been earlier
        terminated provided that Buyer remains eligible to acquire and hold the
        Licenses under applicable decisions, orders or similar rulings of the
        FCC. If the Closing has not occurred by January 27, 2000, the License
        Purchase Agreement shall terminate, unless extended as provided herein,
        and neither party hereto shall have any further obligation to the other
        party to consummate the transactions

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        contemplated thereby. The date for termination of the License Purchase
        Agreement as described in the preceding sentence shall be extended day
        for day for each day beyond December 20, 1999 on which Seller files its
        Notification and Report Form under HSR. Buyer shall have the right to
        extend the License Purchase Agreement for an additional thirty (30)
        days provided that: (i) Buyer advances to the Seller cash from the
        Purchase Price in the amount of one million dollars ($1,000,000); and
        (ii) the Purchase Price is increased by the amount of quarterly interest
        payable on the Licenses to the FCC in January 2000 which is paid by the
        Seller prior to or at the Closing (and the assumption of the Assumed FCC
        Debt by Buyer)."

4. MANAGEMENT AGREEMENT. Paragraph 5(n) of the License Purchase Agreement is
hereby deleted in its entirety.

5. HSR. The first sentence of Section 5(c) is amended to read in its entirety as
follows:

        "The parties shall each file their Notification and Report Forms under
        the HSR not later than December 20, 1999."

6. DE STATUS. Paragraph 6(e) of the License Purchase Agreement is hereby amended
by deleting at the end thereof, the clause "which consent shall have been
granted by Final Order".

7. TERMINATION. Paragraphs 8(a)(1) is deleted in its entirety.

8. EXHIBIT A Purchase of Licenses. Exhibit A to the License Purchase Agreement
is hereby amended to delete the F block license for BTA 178, Greenwood, South
Carolina and to exclude this license from the Licenses being purchased herein.

9. CONSIDERATION. The Buyer and Seller agree to negotiate in good faith about
taking some or all of the consideration otherwise to be paid in cash in common
stock of Leap Wireless International, Inc. If the parties do not agree on all
aspects of such change of consideration, all of such consideration shall be
cash.

Except as expressly amended herein, the parties hereby ratify and confirm the
License Purchase Agreement.

               IN WITNESS WHEREOF, the parties have executed this First
Amendment as of the date first above written.


               Buyer:                 Cricket Holdings, Inc (as assignee of Leap
                                      Wireless International, Inc.)


                                      By:  /s/ S. D. HUTCHESON
                                           -------------------------------------
                                      Its: VICE PRESIDENT
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Seller:                               Airgate Wireless, L.L.C.

                                      By:  /s/ CRIS BLANE
                                           -------------------------------------
                                      Its: MANAGER
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