  Present and future ultra-high-energy-cosmic-ray facilities (e.g., the South
and North components of the Pierre Auger Observatory) and TeV-gamma-ray
telescope arrays (e.g., HESS and CTA) have the potential to set stringent
bounds on the nine Lorentz-violating parameters of nonbirefringent modified
Maxwell theory minimally coupled to standard Dirac theory. A concrete example
is given how to obtain, in the coming decennia, two-sided bounds on the eight
anisotropic parameters at the 10^{-20} level and an upper (lower) bound on the
single isotropic parameter at the +10^{-20} (-10^{-16}) level. Comparison is
made with existing and potential direct bounds from laboratory experiments.
