  We examine the recently proposed relations between black hole entropy and the
topological string in the context of type II/heterotic string dual models. We
consider the degeneracies of perturbative heterotic BPS states. In several
examples with N=4 and N=2 supersymmetry, we show that the macroscopic
degeneracy of small black holes agrees to all orders with the microscopic
degeneracy, but misses non-perturbative corrections which are computable on the
heterotic side. Using these examples we refine the previous proposals and
comment on their domain of validity as well as on the relevance of helicity
supertraces.
