We explain why multi-centered black hole configurations where at least one of
the centers is a large black hole do not contribute to the indexed degeneracies
in theories with N=4 supersymmetry. This is a consequence of the fact that such
configurations, although supersymmetric, belong to long supermultiplets. As a
result, there is no entropy enigma in N=4 theories, unlike in N=2 theories.Comment: 14 page