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

Exhibit 99.1

Mesa-Offshore-Trust

Mesa Offshore Trust Announces No Trust Income for January 2006

MESA OFFSHORE TRUST

JPMorgan Chase Bank, N.A., Trustee	NEWS
	RELEASE

For Immediate Release

Austin, Texas January 20, 2006 - Mesa Offshore Trust (OTC symbol-MOSH) announced that there will be no Trust income distribution for the month of January 2006 for Unitholders of record on January 31, 2006.

No royalty income was reported this month, and trust expenses were $210,347.

As of December 31, 2005 the reserve for Trust expenses, excluding interest receivable, was approximately $1,847,000.

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

700 Lavaca  Austin, TX 78701