  This is the second part of the works on Hausdorff dimensions of Schottky
groups. It has been conjectured that the Hausdorff dimensions of nonclassical
Schottky groups are strictly bounded from below. In this second part of our
works we provide a resolution of this conjecture, we prove that there exists a
universal positive number $\lambda>0$, such that any finitely-generated
non-elementary Kleinian groups with limit set of Hausdorff dimension $<\lambda$
are classical Schottky groups. We will generalize our previous technologies
given in \cite{HS} to prove our general result. Our result can be consider as a
converse to \cite{Doyle}.
