A three-parameter model of neutrino oscillations is presented. It is based on a simple Lorentz- and CPT-violating texture and is consistent with compelling oscillatory signals and null tests involving atmospheric, accelerator, reactor, and solar neutrinos. The solar and atmospheric mixing angles are fixed by the texture at both low and high energies instead of being independent parameters as in most descriptions. One natural feature of the model is anomalous appearance signals in MiniBooNE at low energies, consistent with recent observations for both neutrinos and antineutrinos. Simple texture-preserving extensions of the model can accommodate the recent MINOS anomaly and the LSND signal.