We consider the effect of intermolecular interactions on the optimal size-distribution of N hard spheres that occupy a fixed total volume. When we minimize the free-energy of this system, within the Percus–Yevick approximation, we find that no solution exists beyond a quite low threshold (h » 0.260). Monte Carlo simulations reveal that beyond this density, the size-distribution becomes bimodal. Such distributions cannot be reproduced within the Percus–Yevick approximation. We present a theoretical argument that supports the occurrence of a nonmonotonic size-distribution and emphasize the importance of finite size effects.