  We point out that neutrino events observed at Kamiokande and IMB from SN1987A
disfavor the neutrino oscillation parameters preferred by the LSND experiment.
For $\Delta m^2 > 0$ (the light side), the electron neutrinos from the
neutronization burst would be lost, while the first event at Kamiokande is
quite likely to be due to an electron neutrino. For $\Delta m^2 < 0$ (the dark
side), the average energy of the dominantly $\bar{\nu}_e$ events is already
lower than the theoretical expectations, which would get aggravated by a
complete conversion from $\bar{\nu}_\mu$ to $\bar{\nu}_e$. If taken seriously,
the LSND data are disfavored independent of the existence of a sterile
neutrino. A possible remedy is CPT violation, which allows different mass
spectra for neutrinos and anti-neutrinos and hence can accommodate atmospheric,
solar and LSND data without a sterile neutrino. If this is the case, Mini-BooNE
must run in $\bar{\nu}$ rather than the planned $\nu$ mode to test the LSND
signal. We speculate on a possible origin of CPT violation.
