  We construct local, unitary gauge theories that violate Lorentz symmetry
explicitly at high energies and are renormalizable by weighted power counting.
They contain higher space derivatives, which improve the behavior of
propagators at large momenta, but no higher time derivatives. We show that the
regularity of the gauge-field propagator privileges a particular spacetime
breaking, the one into into space and time. We then concentrate on the simplest
class of models, study four dimensional examples and discuss a number of issues
that arise in our approach, such as the low-energy recovery of Lorentz
invariance.
