A model of neutrino oscillations is presented that has only 3 degrees of freedom and appears compatible with existing data. The model is a subset of the renormalizable sector of the Standard-Model Extension (SME), and it offers a candidate alternative to the standard three-neutrino massive model. All classes of neutrino data are described, including solar, reactor, atmospheric, and LSND oscillations. The disappearance of solar neutrinos is obtained without matter-enhanced oscillations. Quantitative predictions are offered for the ongoing MiniBooNE experiment and for the future experiments OscSNS, NOvA, and T2K.