Mesa Offshore Trust (MOSH) 8-K Mesa Offshore Trust Announces No Trust Income for September 2006

Exhibit 99.1

Mesa-Offshore-Trust

Mesa Offshore Trust Announces No Trust Income for September 2006

MESA OFFSHORE TRUST

JPMorgan Chase Bank, N.A., Trustee

NEWS

RELEASE

For Immediate Release

Austin, Texas September 20, 2006 - Mesa Offshore Trust (OTC symbol-MOSH) announced that there will be no Trust income distribution for the month of September 2006 for Unitholders of record on September 29, 2006.

The Trust did not receive any Royalty income from the Working Interest Owner for the month of September 2006.  The Working Interest Owner withheld $848,519 of proceeds and added this to the abandonment accrual.  The increase in the abandonment accrual is based on revised estimates to abandon all remaining Trust blocks.  Trust expenditures will be approximately $56,000. Trust expenditures in excess of royalty income received will reduce the Trust’s reserve for Trust expenses. As of August 31, 2006 the reserve for Trust expenses, excluding interest receivable, was approximately $1,119,000.

The extent of future distributions from the properties in which the Trust has an interest will continue to be dependent on normal factors associated with oil and gas operations such as oil and gas production levels, prices and associated cost, accruals for future abandonment costs, timing and extent of capital expenditures.

Contact:Mesa Offshore Trust
JPMorgan Chase Bank, N.A., as Trustee
Mike Ulrich
1(800) 852-1422
(512) 479-2562

www.businesswire.com/cnn/mosh.htm

221 West 6th Street Austin, TX 78701