  The feasibility of measuring chiral-odd parton distribution functions in
polarized Drell-Yan and semi-inclusive experiments has renewed theoretical
interest in their study. Models of hadron structure have proven succesful in
describing the gross features of the chiral-even structure functions. Similar
expectations support our study of the transversity parton distributions in the
Isgur-Karl and MIT bag models. We confirm the diverse low x behavior of the
transversity and spin structure functions at the experimental scale and show
that it is fundamentally a consequence of the different behavior under
evolution of these functions. The inequalities of Soffer establish constraints
between data and model calculations of the chiral-odd transversity function.
The approximate compatibility of our model calculations with these constraints
conferes credibility to our estimates.
