  We revamp the constructive enumeration of 1/16-BPS states in the maximally
supersymmetric Yang-Mills in four dimensions, and search for ones that are not
of multi-graviton form. A handful of such states are found for gauge group
SU(2) at relatively high energies, resolving a decade-old enigma. Along the
way, we clarify various subtleties in the literature, and prove a
non-renormalization theorem about the exactness of the cohomological
enumeration in perturbation theory. We point out a giant-graviton-like feature
in our results, and envision that a deep analysis of our data will elucidate
the fundamental properties of black hole microstates.
