  We set constraints on O(E/M) Lorentz Violation in QED in an effective field
theory framework. A major consequence of such assumptions is the modification
of the dispersion relations for electrons/positrons and photons, which in turn
can affect the electromagnetic output of astrophysical objects. We compare the
information provided by multiwavelength observations with a full and
self-consistent computation of the broad-band spectrum of the Crab Nebula. We
cast constraints of order 10^{-5} at 95% confidence level on the lepton Lorentz
Violation parameters.
