  Rashba precession of spins moving along a one-subband quantum channel is
calculated. The quantitative influence of unoccupied higher subbands depends on
the shape of the transversal confinement and can be accounted for
perturbatively. Coulomb interactions are included within the
Tomonaga--Luttinger model with spin-orbit coupling incorporated. Increasing
interaction strength at decreasing carrier density is found to {\sl enhance}
spin precession.
