  We present exact numerical solutions of the damped-driven Jaynes--Cummings
model adapted to describe absorptive optical bistability in the limit of a few
atoms strongly coupled to a high-finesse resonator. We show that the
simplifying semiclassical result for many physical quantities of interest is
well reproduced by the quantum model including even with only a few atoms in
the strongly coupled system. Nontrivial atom-field quantum cross-correlations
show up in the strong-driving limit.
