  Assuming that CPT is violated in the neutrino sector seems to be a viable
alternative to sterile neutrinos when it comes to reconciling the LSND anomaly
with the remainder of the neutrino data. There are different (distinguishable)
ways of incorporating CPT violation into the standard model, including
postulating m different from \bar{m}. Here, I investigate the possibility of
introducing CPT violation via Lorentz-invariance violating effective operators
(``Ether'' potentials) which modify neutrino oscillation patterns like ordinary
matter effects. I argue that, within a simplified two-flavor like oscillation
analysis, one cannot solve the solar neutrino puzzle and LSND anomaly while
still respecting constraints imposed by other neutrino experiments, and comment
on whether significant improvements should be expected from a three-flavor
analysis. If one turns the picture upside down, some of the most severe
constrains on such CPT violating terms can already be obtained from the current
neutrino data, while much more severe constraints can arise from future
neutrino oscillation experiments.

High Energy Physics - Phenomenology