  Present and future ultra-high-energy-cosmic-ray facilities (e.g., the Pierre
Auger Observatory with South and North components) and TeV-gamma-ray telescope
arrays (e.g., HESS or VERITAS and CTA) have the potential to set stringent
indirect bounds on the nine Lorentz-violating parameters of nonbirefringent
modified Maxwell theory minimally coupled to standard Dirac theory.
Theoretically, the most interesting case is isotropic Lorentz violation, which
is described by a single parameter [taken to vanish for the standard
Lorentz-invariant theory]. It appears possible to obtain in the future an upper
(lower) indirect bound on this single isotropic Lorentz-violating parameter at
the +10^{-21} (-10^{-17}) level. Comparison is made with existing and future
direct bounds from laboratory experiments. The possible physics implications of
upper bounds at the 10^{-21} level are discussed.
