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                                                                   Exhibit 10(a)


                             THIRD AMENDMENT TO THE
                       UNITED STATES LIME & MINERALS, INC.

                          EMPLOYEE STOCK OWNERSHIP PLAN


WHEREAS, United States Lime & Minerals, Inc. (the "Corporation") amended and
restated the United States Lime & Minerals, Inc. Employee Stock Ownership
generally effective as of August 1, 1989 (the "Plan"); and

WHEREAS, the Corporation desires to amend the Plan in order to freeze
participation and benefits, merge the Plan with the United States Lime &
Minerals, Inc. 401(k) Profit Sharing Plan (the "401(k) Plan") and comply with
certain changes in the Internal Revenue Code; and

NOW, THEREFORE, pursuant to the powers reserved in Sections 10.01 and 10.03 of
the Plan, the Corporation does hereby amend the Plan effective as of July 31,
1999, unless another date is specified, as follows:


                                       I.

Section 1.01 of the Plan is amended by the addition of the following paragraph
thereto:

         "Notwithstanding anything to the contrary contained herein, in order to
         effectuate the Plan merger with the 401(k) Plan, participation and
         benefits shall be frozen as of the close of business on July 31, 1999.
         The Plan shall be merged with the 401(k) Plan as of the close of
         business on July 31, 1999 and assets shall be transferred as soon as
         administratively possible thereafter."


                                       II.

Effective August 1, 1999, Section 3.01 is hereby deleted in its entirety and the
following inserted in its stead:

         "Section 3.01  Eligibility Requirements.

         Except for Employees described in Section 3.02, all Employees shall be
         eligible to participate in the Plan. Notwithstanding the preceding
         sentence, no Employee shall be eligible to participate under the Plan
         on and after the close of business July 31, 1999."



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                                      III.

Effective August 1, 1998, Sections 4.07(c), 6.02, 6.03, 6.08 are amended by
deleting all references to $3,500 therein and replacing such references with
$5,000. The requirement that the benefit may not at any time have exceeded
$3,500 shall not apply to the $5,000 adjusted limit.

                                       IV.

Effective August 1, 1998, Section 6.08 of the Plan is amended by the addition of
the following language at the end of the first paragraph:

         "The commencement of benefits for a distribution may be less than 30
         days after the receipt of the written explanation of benefit and
         rollover options provided: (A) the Participant has been provided with
         information that clearly indicates that the Participant has at least 30
         days to consider the election; (B) the Participant is permitted to
         revoke any affirmative distribution election at least until the annuity
         starting date, or if later, at any time prior to the expiration of the
         7 day period that begins the day after the explanation is provided to
         the Participant; and (C) the annuity starting date is the date after
         the date that the written explanation was provided to the Participant."

                                 * * * * * * * *

IN WITNESS WHEREOF, the Corporation has caused this instrument to be executed as
of this _________ day of ____________________________, 1999.


                                           UNITED STATES LIME & MINERALS, INC.


                                           By:
                                              ----------------------------------


                                           Title:
                                                 -------------------------------


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