  Let M be a hyperbolizable, nontrivial compression body without toroidal
boundary components. In this paper, we characterize which discrete and faithful
representations of the fundamental group of M into PSL(2,C) are
separable-stable. The set of separable-stable representations forms a domain of
discontinuity for the action of the outer automorphism group of the fundamental
group of M on the PSL(2,C)-character variety of M.
