  A two charge system in string theory preserving eight supercharges can be
described as a small black hole that has zero entropy in the supergravity
approximation, but classical higher derivative corrections produce a finite
entropy in accordance with the prediction of microstate counting. On the other
hand for the same system one can construct smooth horizonless classical
solutions whose geometric quantization describes the individual microstates
which contribute to the entropy. In this note we point out that there is no
duality frame in which the system admits both these classical descriptions.
Thus in a given duality frame horizonless classical solutions and small black
holes are not alternate descriptions of the same system; their contributions
must be added to get a duality invariant result for the macroscopic degeneracy.
We discuss the significance of this observation for the macroscopic computation
of the degeneracy of BPS states for a general system. We also discuss the
relationship between the degeneracy and the index computation and address the
puzzle regarding absence of small black holes in toroidally compactified type
II string theory.
