  It is shown that the Collins mechanism explanation of the transverse
single-spin asymmetries in p^{\uparrow} p -> \pi X leads to a transversely
polarized d quark density Delta_T d(x) which violates the Soffer bound when one
uses several standard forms for the longitudinally polarized d quark density
Delta d(x) obtained from polarized deep inelastic scattering. Imposition of the
Soffer bound with these Delta d(x) yields results in hopeless disagreement with
the data. Remarkably, imposition of the Soffer bound, but using
parametrizations of Delta d(x) that respect the PQCD condition Delta q(x) /
q(x) -> 1 as x -> 1, leads to an excellent fit to most of the data. The
implications for the polarized DIS neutron longitudinal asymmetry A_1^n at
large x are dramatic.
