  The LSND signal for \bar\nu_\mu to \bar\nu_e oscillations has prompted
supposition that there may be a fourth light neutrino or that CPT is violated.
Neither explanation provides a good fit to all existing neutrino data. We
examine the even more speculative possibility that a four-neutrino model with
CPT violation can explain the LSND effect and remain consistent with all other
data. We find that models with a 3+1 mass structure in the neutrino sector are
viable; a 2+2 structure is permitted only in the antineutrino sector.
