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                                                                   EXHIBIT 10.1


                          SUBORDINATED PROMISSORY NOTE


$5,000,000.00                                                Dallas, Texas
                                                             December 27, 2000

               FOR VALUE RECEIVED, the undersigned, UNITED STATES LIME &
MINERALS, INC., a Texas corporation, TEXAS LIME COMPANY, a Texas corporation,
and ARKANSAS LIME COMPANY, an Arkansas corporation (such three corporations
collectively, the "Borrowers"), hereby jointly and severally promise to pay to
the order of INBERDON ENTERPRISES, LTD., a British Columbia corporation (the
"Payee"), on March 27, 2001, the principal sum of Five Million Dollars
(US$5,000,000.00), at the offices of the Payee at 1020-789 West Pender Street,
Vancouver, British Columbia, Canada V6C 1H2, and to pay interest on the unpaid
principal balance hereof from time to time outstanding payable at the time and
in the manner set forth above, accrued at the rate which at all times prior to
maturity shall be nine and three-quarters percent (9 3/4%) per annum and which
from and after maturity shall be eleven and three-quarters percent (11 3/4%) per
annum and shall be payable on demand. All sums payable hereon, whether
principal, interest or otherwise, shall be payable in lawful money of the United
States of America and in immediately available funds, all without any offset,
deduction, recoupment or counterclaim whatsoever. Interest hereon shall be
calculated on the basis of a 360-day year for the actual number of days elapsed.

               The Borrowers reserve the right to prepay this Subordinated
Promissory Note in whole at any time or in portions consisting of $100,000.00 or
an integral multiple thereof from time to time, without premium or penalty but
with interest on the principal amount being prepaid accrued to the date of the
prepayment.

               Interest shall continue to accrue hereon at the rate or rates
hereinabove set forth after, as well as before, the filing of any petition or
application or the commencement of any proceeding or the appointment of any
custodian, receiver, trustee or similar official of the type described in the
following paragraph, in each case whether under state, federal or foreign law.

               In no contingency or event whatsoever shall the aggregate of all
amounts deemed interest hereon exceed the highest rate permissible under any
applicable law which a court of competent jurisdiction shall, in a final
determination, deem applicable hereto. In the event that such a court shall
determine that the Payee or other holder hereof has charged or received interest
hereon in excess of the highest permissible rate, the rate in effect hereon
shall automatically be reduced to the maximum rate permissible under applicable
law and the Payee or other holder hereof shall, at its election, (i) promptly
refund to the Borrowers any interest received by it in excess of the maximum
lawful rate or (ii) shall apply such excess to the principal balance hereof. It
is the intent hereof that the Borrowers not pay or contract to pay, and that the
Payee not




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receive or contract to receive, directly or indirectly in any manner whatsoever,
interest in excess of that which may be paid by the Borrowers under applicable
law.

               If the Borrower (i) shall generally not, or shall be unable to,
or shall admit in writing its inability to pay its debts as such debts become
due; or (ii) shall make a general assignment for the benefit of creditors,
petition or apply to any tribunal for the appointment of a custodian, receiver,
trustee or other similar official for it or a substantial part of its assets; or
(iii) shall commence any proceeding under any bankruptcy, reorganization,
arrangement, readjustment of debt, dissolution or liquidation law or statute of
any jurisdiction, whether now or hereafter in effect; or (iv) shall have any
such petition or application filed or any such proceeding commenced against it,
in which an order for relief is entered or adjudication or appointment is made
and which remains undismissed for a period of sixty (60) days or more; or (v) by
any act or omission shall indicate its consent to, approval of, or acquiescence
in any such petition, application or proceeding, or order for relief, or the
appointment of a custodian, receiver, trustee or other similar official for all
or any substantial part of its properties; or (vi) shall suffer any such
custodianship, receivership or trusteeship to continue undischarged for a period
of sixty (60) days or more, THEN, and in any such event, the outstanding
principal balance hereof, all interest thereon, and all other amounts payable
hereunder shall forthwith become and thereafter be due and payable without
notice, declaration, presentment, demand, protest or notice of any kind, all of
which are hereby expressly waived by the Borrowers.

               If all or any portion of the principal of or interest on this
Subordinated Promissory Note, or other sum owing hereunder, is not paid
punctually when due, the undersigned agrees to pay all costs and expenses
(including without limitation the reasonable fees and disbursements of counsel)
incurred by the Payee or other holder hereof in the collection of this
Subordinated Promissory Note.

               This Subordinated Promissory Note is subordinated on the terms
set forth in the following subparagraphs (a) through (i), inclusive (the terms
set forth in such subparagraphs being herein sometimes referred to collectively
as the "Subordination Provisions"):

                  (a) Any provision of this Subordinated Promissory Note to the
         contrary notwithstanding, but subject, however, to subparagraph (h)
         hereof, the Borrowers hereby agree, and the Payee and each subsequent
         holder hereof (the Payee and any such subsequent holder for the time
         being collectively, the "Holder") by its acceptance hereof hereby
         agrees, that the payment of all of the principal of and all interest,
         fees and other amounts owing hereon or in respect hereof are and shall
         be subject and subordinate to the prior payment in full of (i) all of
         the indebtedness of the Borrowers to the Lenders and the Administrative
         Agent (both as hereinafter defined) under the Credit Agreement, dated
         as of April 22, 1999, as amended (as amended, the "Credit Agreement"),
         by and among the Borrowers, the Lenders referred to therein (the
         "Lenders") and First Union National Bank, as Administrative Agent (the
         "Administrative Agent") and (ii) all of the indebtedness of the
         Borrowers to First Union National Bank (the "Working Capital Lender")
         from time to time outstanding under the Working Capital Facility
         referred to in



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         the Credit Agreement (the "Working Capital Facility"), in each case
         whether such indebtedness is now existing or hereafter arises (all of
         the indebtedness referred to in the foregoing clauses (i) and (ii)
         being herein sometimes referred to collectively as the "Senior Debt"),
         in the manner and to the extent hereinafter set forth.

                  (b) Anything in any agreement executed and delivered by the
         Borrowers or the Payee, or any promissory note executed by the
         Borrowers, or otherwise, to the contrary notwithstanding, but subject,
         however, to subparagraph (h) hereof, the Borrowers shall not make and
         the Holder shall not demand, accept or retain, any payment or
         prepayment of any portion of the indebtedness evidence hereby (such
         indebtedness being hereinafter sometimes referred to collectively as
         the "Subordinated Debt") so long as any part of the Senior Debt shall
         remain outstanding.

                  (c) Subject to subparagraph (h) hereof, in the event of any
         voluntary or involuntary case under the federal bankruptcy laws
         involving any of the Borrowers or any other voluntary or involuntary
         proceeding or action involving any of the Borrowers of the type
         referred to in sections 10.1(i) and (j) of the Credit Agreement (and,
         in the case of any such involuntary case, proceeding or action the same
         shall have continued unstayed and undismissed for the grace period, if
         any, applicable thereto specified in such sections), then and in any
         such event: (i) all of the Senior Debt shall first be paid in full
         before any payment or distribution of any character, whether in cash,
         securities or other property, shall be made in respect of the
         Subordinated Debt; and (ii) any payment or distribution of any
         character payable or deliverable in respect of the Subordinated Debt
         (including any payment or distribution of any other indebtedness of the
         Borrowers or any of them being subordinated to the Subordinated Debt)
         shall be paid or delivered directly to the Administrative Agent for the
         ratable benefit of the Lenders and the Working Capital Lender
         (collectively, the "Senior Creditors") until all Senior Debt shall have
         been paid in full, and the Holder irrevocably authorizes, empowers and
         directs all receivers, custodians, trustees, liquidators, conservators
         and others having authority in the premises to effect all such payments
         and deliveries. The Holder shall execute and deliver to the
         Administrative Agent, for the ratable benefit of the Senior Creditors,
         all such further instruments confirming the authorization referred to
         in the preceding sentence as the Administrative Agent or the Working
         Capital Lender may reasonably request.

                  (d) In the event that any of the Borrowers shall make an
         assignment for the benefit of creditors or any proceedings shall be
         commenced by or against the Borrowers or any of them under any
         bankruptcy, reorganization, readjustment of debt, arrangement,
         dissolution, receivership, liquidation or insolvency law or statute now
         or hereafter in effect, then and in any such event and at any time
         thereafter the Holder will, upon the written request of the
         Administrative Agent or the Working Capital Lender and at the expense
         of the Senior Creditors, use reasonable efforts to prove, enforce and
         endeavor to obtain payment of the aggregate outstanding amount of all
         unpaid Subordinated Debt payments due and payable, or thereafter
         becoming due and payable from the affected


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         Borrower or Borrowers to the Holder, and, subject to subparagraph (h),
         will turn over to the Administrative Agent, for the ratable benefit of
         the Senior Creditors, in precisely the form received, any payment of
         any kind or character received on account of such Subordinated Debt for
         application to the payment of any indebtedness, liabilities and
         obligations then existing of the Borrowers to the holders of the Senior
         Debt or any of them. Subject to subparagraph (h), in the event that the
         Holder shall fail to take any such action properly requested by the
         Administrative Agent or the Working Capital Lender, the Administrative
         Agent may, as attorney-in-fact for the Holder but on prior notice to
         the Holder, take such action on behalf of the Holder, but for the use
         and benefit of the Senior Creditors pro rata, and the Holder hereby
         appoints the Administrative Agent as its attorney-in-fact to demand,
         sue for, collect and receive every such payment and distribution and
         give acquittance therefor and to file claims and to take such other
         proceedings in the Administrative Agent"s own name or in the name of
         the Holder or otherwise, and to vote, give consent and take any other
         steps with regard thereto, all as the Administrative Agent may deem
         necessary or advisable for the enforcement of these Subordination
         Provisions; and the Holder, by its acceptance hereof hereby agrees to
         execute and deliver to the Agent for the ratable benefit of the Senior
         Creditors such additional powers of attorney, assignments and other
         instruments as may reasonably be requested by the Administrative Agent
         or the Working Capital Lender in order to enable the Administrative
         Agent to enforce any and all claims upon or with respect to the
         aforesaid Subordinated Debt and to collect and give any and all
         payments or distributions which may be payable or deliverable at any
         time upon or with respect to such Subordinated Debt.

                  (e) In case cash, securities or other property otherwise
         payable or deliverable to the Holder shall have been applied pursuant
         to the provisions of the preceding paragraph to the payment of Senior
         Debt, and if the Senior Debt shall have been paid in full, then and in
         any such case the Holder shall be subrogated to any rights of the
         Administrative Agent or the Senior Creditors to receive any further
         payments or distributions applicable to the Senior Debt, until the
         Holder shall have been paid in full. No such payments or distributions
         received by the Holder by reason of such subrogation, of cash,
         securities or other property which otherwise would be paid or
         distributed to the Administrative Agent or the Senior Creditors, shall,
         as between the Borrower and its creditors other than the Senior
         Creditors, on the one hand, and the Holder on the other hand, be deemed
         to be a payment by any Borrower on account of the Subordinated Debt.

                  (f) Each Holder by its acceptance hereof hereby (i) waives any
         and all notices of the acceptance of these Subordination Provisions or
         of the creation, renewal, extension or accrual, now or at any time in
         the future, of any indebtedness, liabilities or obligations of any
         Borrower to any Senior Creditor or of the reliance of any Senior
         Creditor on these Subordination Provisions, (ii) consents that, without
         notice to or further assent by it, the indebtedness, liabilities or
         obligations of the Borrowers or of any other party with respect to such
         indebtedness, liabilities and obligations may from time to time, in
         whole or in part, be renewed, extended, modified or released by the
         obligee with respect to such indebtedness, liabilities or obligations
         as the case may be, as such obligee may deem advisable, (iii) consents
         that the Credit Agreement or the Working Capital Facility, or both, or
         any other instrument or document executed and delivered in connection
         with any of them, may from time to time, in whole or in


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         part, be (x) renewed, extended, modified or released by the
         Administrative Agent or the Working Capital Lender, as the case may be,
         as it may deem advisable and (y) amended, modified, supplemented or
         terminated, (iv) consents that any collateral security for any of such
         indebtedness, liabilities and obligations may from time to time, in
         whole or in part, be exchanged, sold or surrendered by the
         Administrative Agent or the Working Capital Lender, as the case may be,
         as it may deem advisable, and (v) consents that the Administrative
         Agent or the Working Capital Lender, as the case may be, may take any
         other action it may deem necessary or appropriate in connection with
         such indebtedness, liabilities and obligations, all without in any
         manner or to any extent impairing or affecting the obligations of the
         Borrowers and the Holder contained in these Subordination Provisions.

                  (g) If, notwithstanding the provisions of this Subordinated
         Promissory Note any payment or distribution of any character (whether
         in cash, securities or other property) or any security shall be
         received by the Holder from any of the Borrowers in contravention of
         the terms of this Subordinated Promissory Note, such payment,
         distribution or security shall not be commingled with any other assets
         of the Holder, shall be held in trust for the benefit of the Senior
         Creditors and shall be paid over or delivered and transferred to the
         Administrative Agent, or its representative, for application to the
         payment pro rata of all Senior Debt remaining unpaid, until all of the
         Senior Debt shall have been paid in full.

                  (h) Any provision of this Subordinated Promissory Note to the
         contrary notwithstanding, all or any part of the indebtedness,
         principal, interest or otherwise, evidenced hereby may be freely paid
         or prepaid in whole at any time or in portions as hereinabove provided
         from time to time, without any consent, authorization or approval of
         any Senior Creditor or other person, solely out of the proceeds of the
         issuance by the Borrowers or any of them of any shares of the capital
         stock of the Borrowers or any one or more of them, or any obligations
         of the Borrowers or any one or more of them subordinated on like terms
         with these Subordination Provisions or on terms otherwise acceptable to
         the Required Lenders and the Working Capital Lender.



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                  (i) The foregoing provisions of subparagraphs (a) through (h)
         are solely for the purpose of defining the relative rights and
         priorities of the Payee and all subsequent holders hereof from time to
         time, on the one hand, and the Senior Creditors, on the other hand,
         and, subject to the rights of the Senior Creditors as aforesaid,
         nothing herein contained shall affect the obligations of the Borrowers,
         which obligations are absolute and unconditional, to pay to the Holder,
         in each case punctually when due, all of the principal of, interest on
         and other amounts owing in respect of this Subordinated Promissory Note
         strictly in accordance with the terms hereof. The provisions of these
         subparagraphs (a) through (i) may not be amended or terminated orally,
         but may be amended or terminated only in writing signed by the
         Borrowers, the Holder, the Administrative Agent and the Working Capital
         Lender or their respective successors or assigns. No waiver of any term
         or provision of this Subordinated Promissory Note shall be effective
         unless it is in writing, signed by the party or parties against whom
         such waiver is sought to be enforced, and making specific reference to
         this Subordinated Promissory Note. This Subordinated Promissory Note
         shall inure to the benefit of the holders of the Senior Debt and their
         successors and assigns and shall be binding upon the Borrowers and the
         Holder and their respective successors and assigns.

               Presentment for payment, demand, dishonor, protest and notice of
dishonor and of protest are all hereby waived by the Borrowers and all
endorsers, if any, hereon.

               This Subordinated Promissory Note shall be governed by and
construed in accordance with the laws of the Commonwealth of Pennsylvania
without reference to the conflicts or choice of law principles thereof.

               IN WITNESS WHEREOF, the Borrowers have caused this Subordinated
Promissory Note to be duly executed in their names by their proper corporate
officer and their seals, if any, to be affixed hereto on the day and year first
hereinabove set forth.

                                   UNITED STATES LIME & MINERALS, INC.
                                   TEXAS LIME COMPANY
                                   ARKANSAS LIME COMPANY


                                   By: /s/ TIMOTHY W. BYRNE
                                      -----------------------------------------
                                      Timothy W. Byrne
                                      President of each such corporation