Measurements of the production of high-pT direct photons by a 515 GeV/c π- beam and 530 and 800 GeV/c proton beams in interactions with Be and H 2 targets are presented. The data span the kinematic ranges of 3.5 < pT < 12 GeV/c in transverse momentum and 1.5 units in rapidity. The inclusive direct-photon cross sections are compared with NLO pQCD calculations and expectations based on a phenomenological parton-kT model.