  Constraints on possible Lorentz symmetry violation (LV) of order E/M_Planck
for electrons and photons in the framework of effective field theory (EFT) are
discussed. Using (i) the report of polarized MeV emission from GRB021206 and
(ii) the absence of vacuum \v{C}erenkov radiation from synchrotron electrons in
the Crab nebula, we improve previous bounds by 10^-10 and 10^-2 respectively.
We also show that the LV parameters for positrons and electrons are different,
discuss electron helicity decay, and investigate investigate how prior
constraints are modified by the relations between LV parameters implied by EFT.
