  The bicycle model of Lorentz noninvariant neutrino oscillations without
neutrino masses naturally predicts maximal mixing and a 1/E dependence of the
oscillation argument for $\nu_\mu \to \nu_\tau$ oscillations of atmospheric and
long-baseline neutrinos, but cannot also simultaneously fit the data for solar
neutrinos and KamLAND. We examine all nineteen possible structures of the
Standard Model Extension for Lorentz noninvariant oscillations of massless
neutrinos that naturally have a 1/E dependence at high neutrino energy. Due to
the lack of any evidence for direction dependence, we consider only
direction-independent oscillations. Although we find a number of models with a
1/E dependence for atmospheric and long-baseline neutrinos, none can also
simultaneously fit solar and KamLAND data.
