  Gluon bremsstrahlung in scattering events with high transverse momentum jets
is expected to increase markedly with the hardness (sum E_T) of the primary
event. Within perturbative QCD we estimate a probability of order unity to see
additional minijets with E_T >~ 15 GeV in ``dijet'' events with sum E_T > 400
GeV. The veto of such minijets is a promising background rejection tool for the
Higgs search at the LHC.
