  Recent studies have shown that two widely-used mechanisms for
single-transverse-spin asymmetries based on either twist-three contributions or
on transverse-momentum-dependent (Sivers) parton distributions become identical
in a kinematical regime of overlap. This was demonstrated for the so-called
soft-gluon-pole and hard-pole contributions to the asymmetry associated with a
particular quark-gluon correlation function in the nucleon. In this paper,
using semi-inclusive deep inelastic scattering as an example, we extend the
study to the contributions by soft-fermion poles and by another independent
twist-three correlation function. We find that these additional terms organize
themselves in such a way as to maintain the mutual consistency of the two
mechanisms for single-spin asymmetries.
