<PAGE>   1
                                                                    Exhibit 10.1


                             INTERVOICE-BRITE, INC.

                FIRST AMENDMENT TO THE THIRD AMENDED AND EXTENDED
                              EMPLOYMENT AGREEMENT

         This First Amendment to the Third Amended and Extended Employment
Agreement as of June 26, 2000 by and between InterVoice-Brite, Inc., a Texas
corporation formerly known as InterVoice, Inc. with its principal executive
offices at 17811 Waterview Parkway, Dallas, Texas 75252 (the "Company") and
Daniel D. Hammond, the "Employee").

                              W I T N E S S E T H:

         WHEREAS, the Employee is presently employed by the Company pursuant to
that certain Third Amended and Extended Employment Agreement dated August 17,
1999 between the Company and the Employee (the "Agreement"); and

         WHEREAS, Employee and the Company desire to amend certain terms of the
Agreement to, among other things, change the Employee's title, duties and adjust
his annual base salary.

         NOW, THEREFORE, in consideration of the premises and mutual covenants
herein, and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, and subject to the terms and
conditions hereinafter set forth, the parties hereto agree as follows:

         1. Paragraph 1 of the Agreement captioned "Definitions" is hereby
amended by deleting definitions of (a) "Applicable EPS Bonus Percentage" and (b)
"Applicable Revenue Bonus Percentage" entirely.

         2. Paragraph 4(a) of the Agreement captioned "Base Salary" is hereby
deleted in its entirety and the following is substituted in its place.

                  4(a) Base Salary. For all services rendered by the Employee
                       under this Agreement, the Company shall pay the Employee
                       a base salary of $240,000 per year. Such salary shall be
                       payable in equal monthly installments in accordance with
                       the customary payroll policies of the Company in effect
                       at the time such payment is made, or as otherwise
                       mutually agreed upon. Effective as of March 1 of each
                       year during the term hereof, the Compensation Committee
                       of the Company shall review Employee's performance for
                       the prior fiscal year and make such adjustments in base
                       salary from time to time at their discretion as the
                       Employee and the Company may agree.

         3. Paragraph 4(b) of the Agreement captioned "Annual Bonus" is hereby
deleted in its entirety.


                                        1

<PAGE>   2


         4. Paragraph 5(a) of the Agreement captioned "Position and Duties" is
hereby deleted in its entirety and the following is substituted in its place.

                  5(a) Position and Duties. Employee shall serve as the Chairman
                       of the Board of the Company, accountable only to the
                       Board of Directors of the Company and subject to the
                       authority of such board and shall have such other powers
                       and duties as may from time to time be prescribed by such
                       board, provided that such duties are reasonable and
                       customary for a Chairman of the Board of a public
                       company.

         5. Paragraph 5(b) of the Agreement captioned "Extent of Services and
Situs" is hereby deleted in its entirety and the following is substituted in its
place.

                  5(b) Extent of Services and Situs. The Employee shall devote a
                       sufficient amount of his business time, attention and
                       energy to the business and affairs of the Company as is
                       necessary to carry out his duties described in paragraph
                       5(a) above and shall not during the term of his
                       employment under this Agreement engage in any other
                       business activity which could constitute a conflict of
                       interest, whether or not such business activity is
                       pursued for gain, profit, or other pecuniary advantage.
                       This shall not be construed as preventing the Employee
                       from managing his current investments or investing his
                       assets in such form or manner as will not require any
                       services on the part of the Employee in the operation and
                       the affairs of the companies in which such investments
                       are made, subject to the provisions of Sections 6 and 27.
                       The Employee shall not be required to change the
                       principal place of his employment to a location which is
                       more than 15 miles further away from his principal
                       residence than such principal place of employment at the
                       time of the execution of this Agreement.

         6. The entire Agreement is amended by deleting entirely reference to
"Annual Bonus" wherever it appears.

         7. All of the provisions of the Agreement not specifically amended,
deleted or modified by this First Amendment are hereby ratified in their
entirety and shall remain in full force and effect.


                                        2

<PAGE>   3


         IN WITNESS WHEREOF, the parties have executed this First Amendment to
the Agreement on the day first above written.

                                        COMPANY:

                                        INTERVOICE-BRITE, INC.

                                        By:
                                             ---------------------------------
                                        Name:
                                               -------------------------------
                                        Title:
                                                ------------------------------

                                        EMPLOYEE:

                                        --------------------------------------
                                        DANIEL D. HAMMOND


                                        3