  Based on the Kompaneets approximation, we develop a robust methodology to
calculate spectral redistribution via inelastic neutrino-nucleon scattering in
the context of core-collapse supernova simulations. The resulting equations
conserve lepton number to machine precision and scale linearly, not
quadratically, with number of energy groups. The formalism also provides an
elegant means to derive the rate of energy transfer to matter which, as it
must, automatically goes to zero when the neutrino radiation field is in
thermal equilibrium. Furthermore, we derive the next-higher-order in
{\epsilon}/mc2 correction to the neutrino Kompaneets equation. Unlike other
Kompaneets schema, ours also generalizes to the case of anisotropic angular
distributions, while retaining the conservative form that is a hallmark of the
classical Kompaneets equation. Our formalism enables immediate incorporation
into supernova codes that follow the spectral angular moments of the neutrino
radiation fields.
