Recently, Ooguri, Strominger and Vafa have proposed to identify the macroscopic Bekenstein-Hawking-Wald entropy of extremal charged Black Holes in type II string compactified on a Calabi-Yau threefold, with the all order microscopic entropy in a specific statistical ensemble. We present a test of this conjecture in the case of 'small' black holes (which have zero Bekenstein-Hawking entropy at tree level, but obtain a non-zero entropy after quantum corrections) using heterotic / type II duality. We find a remarkable agreement to all orders in a class of N=2 and N=4 compactifications. Nevertheless, the OSV proposal misses non-perturbative corrections which are computable on the heterotic side. We comment on possible improvements of this proposal.