  We show that a hierarchical CPT violating neutrino spectrum can
simultaneously accommodate all published neutrino data, including the LSND
result, with a total chi^2 which is almost identical to the CPT conserving best
fit. In our scenario the oscillation signal seen by the KamLAND experiment in
antineutrinos is independent of the LMA solar oscillation signal seen in
neutrinos. A larger antineutrino mass splitting accounts for the LSND signal
and also contributes to atmospheric oscillations. Because of this feature,
there is some tension between our model and certain Super-K atmospheric
results. Thus, if LSND did not exist, our model would survive only at the 99%
confidence level; with LSND, our model is (essentially) statistically
equivalent to the CPT conserving best fit.
