  Static solutions of large-$N$ quantum dilaton gravity in $1+1$ dimensions are
analyzed and found to exhibit some unusual behavior. As expected from previous
work, infinite-mass solutions are found describing a black hole in equilibrium
with a bath of Hawking radiation. Surprisingly, the finite mass solutions are
found to approach zero coupling both at the horizon and spatial infinity, with
a ``bounce'' off of strong coupling in between. Several new zero mass solutions
-- candidate quantum vacua -- are also described.
