Self-induced flavor conversions of supernova (SN) neutrinos can strongly modify the flavor-dependent fluxes. We perform a linearized flavor stability analysis with accretion-phase matter profiles of a 15M[symbol: see text] spherically symmetric model and corresponding neutrino fluxes. We use realistic energy and angle distributions, the latter deviating strongly from quasi-isotropic emission, thus accounting for both multiangle and multienergy effects. For our matter and neutrino density profile we always find stable conditions: flavor conversions are limited to the usual Mikheyev-Smirnov-Wolfenstein effect. In this case one may distinguish the neutrino mass hierarchy in a SN neutrino signal if the mixing angle θ13 is as large as suggested by recent experiments.