The question of a possible container shape dependence of the sedimentation velocity in a homogeneous suspension is reexamined. To this end we develop a statistical theory of suspensions based on low-Reynolds-number hydrodynamics of spherical particles in a container. It is shown, to first order in the volume fraction, that in an arbitrary vessel the relative sedimentation velocity is shape independent, but that at the same time shape-dependent convection occurs. The theory forms a bridge between earlier calculations for special geometries by Beenakker and Mazur and a phenomenological theory recently proposed by NoziEres.