  It is studied the possibility of direct extraction of the transversity and
its accompanying T-odd parton distribution function (PDF) from Drell-Yan (DY)
processes with unpolarized pion beam and with both unpolarized and transversely
polarized proton targets. At present, such a measurement can be performed on
the COMPASS experiment at CERN. The preliminary estimations performed for
COMPASS kinematic region demonstrate that it is quite real to extract both
transversity and its accompanying T-odd PDF in the COMPASS conditions
