  We develop a technique to investigate the possibility that some of the
recently discovered ultra-faint dwarf satellites of the Milky Way might be cusp
caustics rather than gravitationally self-bound systems. Such cusps can form
when a stream of stars folds, creating a region where the projected 2-D surface
density is enhanced. In this work, we construct a Poisson maximum likelihood
test to compare the cusp and exponential models of any substructure on an equal
footing. We apply the test to the Hercules dwarf (d ~ 113 kpc, M_V ~ -6.2, e ~
0.67). The flattened exponential model is strongly favored over the cusp model
in the case of Hercules, ruling out at high confidence that Hercules is a cusp
catastrophe. This test can be applied to any of the Milky Way dwarfs, and more
generally to the entire stellar halo population, to search for the cusp
catastrophes that might be expected in an accreted stellar halo.
