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The nature of pulses resulting from alpha, beta, gamma, and neutron irradiation of Hornyak buttons has been examined under various conditions, including the use of light filters and both fast and slow electronics. Tentative conclusions about the mechanism of their origin are reached. Pulses from Compton recoils originate in the matrix and light transmitting media of the Hornyak button and phototube. Such pulses are of short duration, being similar in shape to photomultiplier noise pulses, in contrast to the 70-nanosecond decay of the fastest component of ZnS(Ag) fluorescence. A relatively simple, passive anticoincidence network is described which allows fast cancellation of the gamma-induced short pulses while passing the zinc sulfide scintillation with adequate efficiency. Rise time of the pulses emerging from the background suppression circuit is about 7 nsec. This network, in conjunction with a distributed amplifier, tunnel diode discriminator, and other fast electronic equipment is usel to select fission neutrons in coincidence with fission events.