  We consider the single-spin azimuthal asymmetries recently measured at the
HERMES experiment for charged pions produced in semi-inclusive deep inelastic
scattering of leptons off longitudinally polarized protons. Guided by the
experimental results and assuming a vanishing twist-2 transverse quark spin
distribution in the longitudinally polarized nucleon, denoted as ``reduced
twist-3 approximation'', a self-consistent description of the observed
single-spin asymmetries is obtained. In addition, predictions are given for the
z dependence of the single target-spin asymmetry.
