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                                                                   EXHIBIT 10.12


                                                                         ANNEX A











                AMENDMENTS TO 1991 NONQUALIFIED STOCK OPTION PLAN

                           FOR NON-EMPLOYEE DIRECTORS




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                        AMENDMENT TO THE SOUTHDOWN, INC.
                       1991 NONQUALIFIED STOCK OPTION PLAN
                           FOR NON-EMPLOYEE DIRECTORS


                              W I T N E S S E T H:


     WHEREAS, Southdown, Inc. (the "Company") presently maintains the Southdown,
Inc. 1991 Nonqualified Stock Option Plan for Non-Employee Directors which became
effective on February 14, 1991 and was amended and restated as of November 21,
1996 (the "Plan"); and

     WHEREAS, the Company, pursuant to paragraph 15 of the Plan, has the right
to amend the Plan from time to time subject to certain limitations.

     NOW, THEREFORE, in order to increase the number of shares of Common Stock
(as defined in the Plan) which may be acquired under a Subsequent Option (as
defined in the Plan), and to make certain other amendments, the Plan is hereby
amended in the following manner:

     1. The first sentence of paragraph 3 of the Plan is hereby amended in its
entirety to read as follows:

     3. STOCK RESERVED FOR THE PLAN.

        Subject to adjustment as provided in paragraph 11, the shares subject
     to the Plan shall consist of 725,000 unissued shares of Common Stock or
     previously issued shares reacquired and held by the Company and such amount
     of shares shall be and is hereby reserved for issuance pursuant to this
     Plan.

     2. The first paragraph of paragraph 4 of the Plan is hereby amended in its
entirety to read as follows:

     4. GRANT OF OPTIONS.

        Each director of the Company who is not otherwise an employee of the
     Company or any of the Company's subsidiaries (as defined in Section 424(f)
     of the Internal Revenue Code of 1986) (hereinafter referred to as an
     "Eligible Director", which term shall include any transferee permitted
     pursuant to paragraph 9 below) shall be granted one option to acquire
     10,000 shares of Common Stock ("Initial Option"), in the case of an
     Eligible Director serving on the Board on the date of adoption of the Plan
     by the Board, on such date of adoption and in all other cases on the date
     of such director's first election to the Board. Beginning on the Annual
     Meeting of Shareholders held in 1999, and on the date of each Annual
     Meeting of Shareholders thereafter where an Eligible Director continues to
     serve as a Director of the Company after such meeting, (i) each Eligible
     Director who is neither a chairman of one of the committees of the Board
     nor the Chairman of the Board shall automatically be granted an additional
     option to acquire

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     7,500 shares of Common Stock, (ii) each Eligible Director who is a chairman
     of one of the committees of the Board, but is not Chairman of the Board,
     shall automatically be granted an additional option to acquire 8,000 shares
     of Common Stock, and (iii) the Chairman of the Board of Directors shall
     automatically be granted an additional option to acquire 26,000 shares of
     Common Stock (each annual grant under (i), (ii) and (iii) for an Eligible
     Director is referred to hereinafter as a "Subsequent Option"). The options
     granted to Eligible Directors shall be automatic, nondiscretionary, and
     subject to the following conditions and limitations in addition to those
     set forth elsewhere in this Plan: (x) the exercise price of each option
     shall be equal to the greater of the par value of the Common Stock or 100%
     of the fair market value of the Common Stock on the Date of Grant; (y) each
     option shall become exercisable six months after the Date of Grant; (z)
     notwithstanding clause (y) above, each option shall be fully exercisable
     upon the death or disability of the Eligible Director while serving as a
     Director of the Company or upon a Change in Control of the Company while
     serving as a Director of the Company.

     3. This Amendment shall be effective upon the date of its adoption by the
Board of Directors of the Company (the "Board"), provided that this Amendment is
approved within twelve months thereafter by a majority of the votes cast by the
stockholders of the Company on the proposal, as long as at least 50% of the
outstanding shares vote on the proposal.

     4. This Amendment to the Plan was approved by the Board on March 25, 1999.
Except as provided herein, the Plan remains unchanged and in full force and
effect.


Approved:                                    Date:
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