There is a unique Lorentz-violating modification of the Maxwell theory of photons, which maintains gauge invariance, CPT, and renormalizability. Restricting the modified-Maxwell theory to the isotropic sector and adding a standard spin-1 2 Dirac particle p ± with minimal coupling to the nonstandard photon γ, the resulting modified-quantum-electrodynamics model involves a single dimensionless "deformation parameter," κ tr . The exact tree-level decay rates for two processes have been calculated: vacuum Cherenkov radiation p ± → p ± γ for the case of positive κ tr and photon decay γ → p + p − for the case of negative κ tr . From the inferred absence of these decays for a particular high-quality ultrahigh-energy-cosmic-ray event detected at the Pierre Auger Observatory and a well-established excess of TeV gamma-ray events observed by the High Energy Stereoscopic System telescopes, a two-sided bound on κ tr is obtained, which improves by eight orders of magnitude upon the best direct laboratory bound. The implications of this result are briefly discussed.