  Neutrinos may mix with ultralight fermions, which gives flavor oscillations,
and with heavier fermions, which yields short distance flavor change. I
consider the case where both effects are present. I show that in the limit
where a single oscillation length is experimentally accessible, the effects of
heavier fermions on neutrino oscillations can generically be accounted for by a
simple formula containing four parameters, including observable CP violation. I
consider the anomalous LSND and MiniBooNE results, and show that these can be
fit in a model with CP violation and two additional sterile neutrinos, one in
the mass range between 0.1 and 20 eV, and the other with mass between 33 eV and
40 GeV. I also show that this model can avoid conflict with constraints from
existing null short baseline experimental results.
