  In a previous paper [Phys. Rev. A 72, 033415 (2005)], it was shown that
sub-Doppler cooling occurs in a standing-wave Raman scheme (SWRS) that can lead
to reduced period optical lattices. These calculations are extended to allow
for non-zero detuning of the Raman transitions. New physical phenomena are
encountered, including cooling to non-zero velocities, combinations of Sisyphus
and "corkscrew" polarization cooling, and somewhat unusual origins of the
friction force. The calculations are carried out in a semi-classical
approximation and a dressed state picture is introduced to aid in the
interpretation of the results.
