Exhibit 99.1

NEWS RELEASE
                                                       Dorchester Minerals, L.P.
Release Date: June 29, 2006                       3838 Oak Lawn Ave., Suite 300
                                                        Dallas, Texas 75219-4541
Contact:  Casey McManemin                               Telephone (214) 559-0300
Facsimile (214) 559-0301

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 DORCHESTER MINERALS, L.P. ANNOUNCES CONSUMMATION OF ARKANSAS LEASE TRANSACTION

      DALLAS, TEXAS -- Dorchester Minerals, L.P. announced today the successful
consummation of a series of transactions pursuant to which the Partnership
leased its interest in lands located in the Fayetteville Shale Trend of Northern
Arkansas to a large independent oil and gas exploration company.

      As previously announced, the Partnership entered into an agreement on
March 30, 2006 to lease its interest in certain lands located in Cleburne,
Conway, Faulkner, Franklin, Johnson, Pope, Van Buren, and White Counties,
Arkansas.  The Partnership received a non-refundable payment in the amount of
$616,000, which amount was included in the Partnership's first quarter
distribution to unitholders. The agreement provided 90 days for title due
diligence and documentation.

     On June 28, 2006 the Partnership leased its average 8.6% mineral interest
in 179 sections of land in these eight counties and received additional payments
totaling $5,535,000. This amount will be included in the second quarter
distribution to unitholders. The leases reflect one-fourth royalty and five year
primary terms.  Assuming the lands are pooled into 640 acre units, the
Partnership will own an average 2.1% net royalty interest in each well drilled
in these sections.

     In addition to the basic lease terms, the Partnership has the option to
participate for an average 3.5% net working interest in 117 of 179 sections.
The Partnership has exercised this option in one section. In addition, the
Partnership elected not to lease its interest totaling 260 net mineral acres in
four sections located in the Gravel Hill Field area of Conway County. The
Partnership's optional working interest in the leased lands and the unleased
mineral interest in the Gravel Hill Field area have been assigned to Dorchester
Minerals Operating, L.P. pursuant to the existing Net Profits Interest
agreements.

     Dorchester Minerals, L.P. is a Dallas based owner of producing and
non-producing crude oil and natural gas mineral, royalty, overriding royalty,
net profits, and leasehold interests and its common units trade on the Nasdaq
Stock Market under the symbol DMLP.

FORWARD-LOOKING STATEMENTS

     Portions of this document may constitute "forward-looking statements" as
defined by federal law. Such statements are subject to certain risks,
uncertainties and assumptions. Should one or more of these risks or
uncertainties materialize, or should underlying assumptions prove incorrect,
actual results may vary materially from those anticipated, estimated or
projected. Examples of such uncertainties and risk factors include, but are not
limited to, changes in the price or demand for oil and natural gas, changes in
the operations on or development of the Partnership's properties, changes in
economic and industry conditions and changes in regulatory requirements
(including changes in environmental requirements) and the Partnership's
financial position, business strategy and other plans and objectives for future
operations. These and other factors are set forth in the Partnership's filings
with the Securities and Exchange Commission.