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A two charge system in string theory preserving eight supercharges can bedescribed as a small black hole that has zero entropy in the supergravityapproximation, but classical higher derivative corrections produce a finiteentropy in accordance with the prediction of microstate counting. On the otherhand for the same system one can construct smooth horizonless classicalsolutions whose geometric quantization describes the individual microstateswhich contribute to the entropy. In this note we point out that there is noduality frame in which the system admits both these classical descriptions.Thus in a given duality frame horizonless classical solutions and small blackholes are not alternate descriptions of the same system; their contributionsmust be added to get a duality invariant result for the macroscopic degeneracy.We discuss the significance of this observation for the macroscopic computationof the degeneracy of BPS states for a general system. We also discuss therelationship between the degeneracy and the index computation and address thepuzzle regarding absence of small black holes in toroidally compactified typeII string theory.

Two Charge System Revisited: Small Black Holes or Horizonless Solutions?