  Observations of the synchrotron and inverse Compton emissions from
ultrarelativistic electrons in astrophysical sources can reveal a great deal
about the energy-momentum relations of those electrons. They can thus be used
to place bounds on the possibility of Lorentz violation in the electron sector.
Recent $\gamma$-ray telescope data allow the Lorentz-violating electron
$c^{\nu\mu}$ parameters to be constrained extremely well, so that all bounds
are at the level of $7\times 10^{-16}$ or better.
