  Searches for anisotropies due to Earth's motion relative to a preferred frame
-- modern versions of the Michelson-Morley experiment -- provide precise
verifications of special relativity. We describe other tests, independent of
this motion, that are or can become even more sensitive. The existence of
high-energy cosmic rays places strong constraints on Lorentz non-invariance.
Furthermore, if the maximum attainable speed of a particle depends on its
identity, then neutrinos, even if massless, may exhibit flavor oscillations.
Velocity differences far smaller than any previously probed can produce
characteristic effects at accelerators and solar neutrino experiments.
