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 _ { \scriptscriptstyle CDM } \sim 1.4 - 1.5 .