  A Bayesian likelihood analysis of the stellar density profile shapes of
several dark matter dominated Galactic dwarf spheroidal galaxies (dSphs) has
been completed. This analysis indicates that the inner power law, \rho \propto
r^{-\gamma}, of each of these profiles satisfies \gamma < 1.21 at greater than
99% confidence with a slight preference for \gamma \sim 0.7 . Speculating that
this bound on the stellar profiles may be related to the inner power law of the
underlying dark matter distribution reveals a statistical discrepancy with the
values favoured by recent N-body simulations of cold dark matter (CDM),
\gamma_{CDM} \sim 1.4-1.5 .
