  One of the very small number of serious alternatives to the usual concept of
an astrophysical black hole is the "gravastar" model developed by Mazur and
Mottola; and a related phase-transition model due to Laughlin et al. We
consider a generalized class of similar models that exhibit continuous pressure
-- without the presence of infinitesimally thin shells. By considering the
usual TOV equation for static solutions with negative central pressure, we find
that gravastars cannot be perfect fluids -- anisotropic pressures in the
"crust" of a gravastar-like object are unavoidable. The anisotropic TOV
equation can then be used to bound the pressure anisotropy. The transverse
stresses that support a gravastar permit a higher compactness than is given by
the Buchdahl--Bondi bound for perfect fluid stars. Finally we comment on the
qualitative features of the equation of state that gravastar material must have
if it is to do the desired job of preventing horizon formation.
