POWER OF ATTORNEY

STATE OF TEXAS	     )(

COUNTY OF DALLAS  )(

KNOW ALL MEN BY THESE PRESENTS:

THAT I, Antoine M. Doumet, a Director of United States
Lime & Minerals, Inc., a Texas corporation, hereby constitute and
appoint Timothy W. Byrne  and M. Michael Owens as my true and
lawful attorneys-in-fact and agents, with full power of substitution
and resubstitution, to sign for me and in my name, place, and stead,
in any and all capacities, any and all forms required to be filed by
me pursuant to Section 16(a) of the Securities Exchange Act of
1934 and the rules promulgated thereunder and any and all
amendments to such forms and to file the same with the United States
Securities and Exchange Commission.  I further hereby ratify and
confirm any and all actions, matters, and things that such
attorneys-in-fact and agents shall lawfully do or cause to be done by
virtue of this Power of Attorney and the rights and powers granted
herein.  This Power of Attorney expires on May 31, 2005.

	EXECUTED this 4th day of May, 2004

				/s/ Antoine M. Doumet

STATE OF TEXAS          )(
COUNTY OF DALLAS   )(

	This instrument was acknowledged before me on the 4th day
of May, 2004 by Antoine M. Doumet.

				/s/ Nita Mitchell
				Notary Public
				State of Texas
				My Commission Expires:
				10/12/07