  We construct generalizations of the Calogero-Sutherland-Moser system by
appropriately reducing a classical Calogero model by a subset of its discrete
symmetries. Such reductions reproduce all known variants of these systems,
including some recently obtained generalizations of the spin-Sutherland model,
and lead to further generalizations of the elliptic model involving spins with
SU(n) non-invariant couplings.
