Gluon bremsstrahlung in scattering events with high transverse momentu
m jets is expected to increase markedly with the hardness (Sigma E(T))
of the primary event. Within perturbative QCD we estimate a probabili
ty of order unity to see additional minijets with E(T) greater than or
similar to 15 GeV in ''dijet'' events with Sigma E(T) > 400 GeV. The
veto of such minijets is a promising background rejection tool for the
Higgs search at the LHC.