We consider effects of parton (primarily gluon) bremstrahlung in the initial and final states of high transverse momentum hadron‐hadron scattering. Monte Carlo calculations based on conventional QCD parton branching and scattering processes are presented. The calculations are carried only to the parton level in the final state. We apply the model to the Drell‐Yan process and to high transverse momentum hadron‐hadron scattering triggered with a large aperture calorimeter. We show that the latter triggers are biased in that they select events with unusually large bremstrahlung effects. We suggest that this trigger bias explains the large cross section and non‐coplanar events observed in the NA5 experiment at the SPS.