  We consider a general formalism to compute inclusive polarised and
unpolarised cross sections within pQCD and the factorisation scheme, taking
into account parton intrinsic motion in distribution and fragmentation
functions, as well as in the elementary dynamics. Surprisingly, the intrinsic
partonic motion, with all the correct azimuthal angular dependences, produces a
strong suppression of the transverse single spin asymmetry arising from the
Collins mechanism. As a consequence, and in contradiction with earlier claims,
the Collins mechanism is unable to explain the large asymmetries found in
p(transv. polarised) p --> pion + X at moderate to large Feynman x_F. The
Sivers effect is not suppressed.
