An 18″×18″ plastic well scintillator is used to monitor the escape radiation from a 5″ D NaI well crystal. Coincident events in both scintillators are rejected by means of an anticoincidence circuit. The detectors are mounted in a 2 ton lead and mercury shield so they can be used for the radioassay of low activity samples. Design of electronic equipment used with the plastic scintillators is considered and data presented on the effectiveness of the anticoincidence mantle in improving the performance of the NaI crystal by (a) reducing the Compton spectrum (b) increasing its efficiency as a sum spectrometer and (c) reducing its background spectra. Expressions are derived for the efficiency of the plastic mantle in detecting escape radiation from the NaI crystal and compared to experimental data.