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Image quality in nuclear medicine is a trade-off between image contrast and resolution, since there are conflicting requirements of crystal thickness and collimator-hole dimensions. The sensitivity, or efficiency, which determines the contrast-to-noise ratio, however, is constrained primarily by pulse-mode operation, in which gamma ray interactions are recorded once every deadtime period. Nuclear images also suffer from image blurring due to gamma rays penetrating the collimator septa and due to misplaced pileup events arising from the coincidence detection of Compton-scattered gamma rays. Multi-zone detector architecture (MZDA) and the use of pileup prevention circuitry (PPC) lead to reduction of the detector's effective deadtime, and hence to significant extension of the count-rate range of the camera. This in turn allows the source activity to be increased to make up for sensitivity that will be lost on changing the detector and collimator-hole dimensions to improve spatial resolution. Misplaced pileup suppression (MPS) circuitry, also described in this paper, enables image blurring from Compton-scattered radiation to be reduced to 1/P of its level in a single zone detector, P being the PMT array size. The paper first develops the theoretical relationships relating to the trade-offs between efficiency and resolution, the distribution of scintillation light from interaction points in the crystal, the share of the light exposure of individual PMTs and of clusters of PMTs, and the cross-talk between clusters of PMTs. The paper then presents an outline of the implementation of an S-zone camera with PPC of order 1, based on hexagonal and rectangular arrays of PMTs. A hexagonal array of 331 1.27-cm PMTs, which will have S ap 35 detector-zones on average, can, for instance, use a 1.7-mm thick and 29-cm diameter NaI(Tl) crystal to design a camera with twice the sensitivity of a single-zone camera of the same array size, which will also provide a spatial resolutio- - n of 2.1 mm at the collimator face and 3.4 mm at 10 cm from the collimator face.