  We discuss self-consistent geometries and behavior of dilaton in exactly
solvable models of 2D dilaton gravity, with quantum fields in the Boulware
state. If the coupling $H(\phi)$ between curvature and dilaton $\phi $ is
non-monotonic, backreaction can remove the classical singularity. As a result,
an everywhere regular star-like configuration may appear, in which case the
Boulware state, contrary to expectations, smooths out the system. For monotonic
$H(\phi)$ exact solutions confirm the features found before with the help of
numerical methods: the appearance of the bouncing point and the presence of
isotropic singularity at the classically forbidden branch of the dilaton.
