  In five-dimensional minimal supergravity, there are spherical black holes
with nontrivial topology outside the horizon which have the same conserved
charges at infinity as the BMPV solution. We show that some of these black
holes have greater entropy than the BMPV solution. These spacetimes are all
asymptotically flat, stationary, and supersymmetric. We also show that there is
a limit in which the black hole shrinks to zero size and the solution becomes a
nonsingular "bubbling" geometry. Thus, these solutions provide explicit
analytic examples of placing black holes inside solitons.
