  We discuss ultracompact stellar objects which have multiple necks in their
optical geometry. There are in fact physically reasonable equations of state
for which the number of necks can be arbitrarily large. The proofs of these
statements rely on a recent regularized formulation of the field equations for
static spherically symmetric models due to Nilsson and Uggla. We discuss in
particular the equation of state p=\rho-\rho_s which plays a central role in
this context.
