EXHIBIT 8.2


November 15, 2002

Tremont Corporation
1999 Broadway, Suite 4300
Denver, Colorado 80202

Ladies & Gentlemen:

         We have acted as counsel to the special committee to the board of
directors of Tremont Corporation, a Delaware corporation ("Tremont"), in
connection with the proposed merger (the "Merger") of Valhi Acquisition Corp.
("Valhi Acquisition"), a Delaware corporation and a direct, wholly-owned
subsidiary of Valhi, Inc., a Delaware corporation ("Valhi"), with and into
Tremont. All capitalized terms used but not defined herein have the meanings
ascribed to them in the Agreement and Plan of Merger dated as of November 4,
2002, and the Amendment No. 1 to Agreement and Plan of Merger dated November 12,
2002, both among Valhi, Valhi Acquisition and Tremont (collectively, the "Merger
Agreement"). This opinion is being delivered in connection with the filing with
the Securities and Exchange Commission of the Proxy Statement/Prospectus on Form
S-4 relating to the proposed Merger pursuant to the Merger Agreement (the "Proxy
Statement") to which this opinion appears as an exhibit.

         In acting as counsel to the special committee to the board of directors
of Tremont in connection with the Merger, we have participated in the
preparation of the Merger Agreement and the preparation and filing with the
Securities and Exchange Commission of the Proxy Statement.

         You have requested that we render the opinion set forth in the Proxy
Statement. In rendering such opinion, we have assumed with your consent that (i)
the Merger will be effected in accordance with the Merger Agreement (and
exhibits thereto) and the General Corporation Law of the State of Delaware and
as described in the Proxy Statement, (ii) the representations made by Valhi,
Valhi Acquisition and Tremont in letters provided to us, dated as of the date
hereof (the "Officer's Certificates") are true, correct and complete, and will
be true, correct and complete as of the Effective Time (as if made as of the
Effective Time), (iii) any representations made in such letters "to the best
knowledge of" or similarly qualified are true, correct and complete without such
qualification and (iv) as to all matters as to which any person or entity
represents that it is not a party to, does not have or is not aware of any plan,
intention, understanding or agreement, there is in fact no such plan, intention,
understanding or agreement. We have also assumed that the representations and
warranties contained in the Merger Agreement, and statements as to factual
matters contained in the Proxy Statement, are true, correct and complete as of
the date hereof, and will be true, correct and complete as of the Effective
Time, and that the parties have complied with and, if applicable, will continue
to comply with, the covenants contained in the Merger Agreement.

         The Proxy Statement sets forth our opinion in the section entitled
"Material Federal Income Tax Consequences of the Merger," as to those matters as
to which we are described therein as rendering an opinion, subject to the
limitations and qualifications set forth in such section and herein.

         Our opinion is based on the Internal Revenue Code of 1986, as amended
(the "Code"), Treasury Regulations, administrative interpretations, and judicial
precedents as of the date hereof. It should be noted that statutes, regulations,
judicial decisions and administrative interpretations are subject to change at
any time and, in some circumstances, with retroactive effect and our opinion
could be adversely affected or rendered obsolete by any such change. No ruling
has been or will be sought from the Internal Revenue Service ("IRS") as to the
federal income tax consequences of any matters set forth in the above
discussion. The opinion expressed herein is not binding on the IRS or any court,
and there can be no assurance that the IRS or a court will not disagree with
such opinion. Further, no assurance can be given that future legislative,
judicial or administrative changes would not adversely affect the accuracy of
the conclusions stated herein. Nevertheless, by rendering this opinion we
undertake no responsibility to advise you of any new developments in the
application or interpretation of the federal tax laws. Because this opinion is
being delivered prior to the Effective Time of the Merger, it must be considered
prospective




Tremont Corporation
November 15, 2002
Page 2

and dependent on future events. There can be no assurance that changes in the
law will not take place that could affect the U.S. federal income tax
consequences of the Merger or that contrary positions may not be taken by the
IRS.

         This opinion is furnished to you solely for use in connection with the
Proxy Statement. We hereby consent to the filing of this opinion as an exhibit
to the Proxy Statement. We also consent to the reference to our firm name
wherever appearing in the Proxy Statement with respect to the discussion of the
material federal income tax considerations of the Merger, and any amendment
thereto. In giving this consent, we do not thereby admit that we are in the
category of persons whose consent is required under Section 7 of the Securities
Act of 1933, as amended, or the rules and regulations of the Securities and
Exchange Commission thereunder, nor do we thereby admit that we are experts with
respect to any part of such Proxy Statement within the meaning of the term
"experts" as used in the Securities Act of 1933, as amended, or the rules and
regulations of the Securities and Exchange Commission thereunder.

                                      Very truly yours,

                                      PIPER RUDNICK LLP