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In a positron emission tomograph the ratio of true-to-random coincidences decreases at elevated count rates, thereby causing a degraded image. Efficiency simulations of a representative sample configuration show that for brain cameras, the high sensitivity range of BGO systems can be extended by using an optimized coincidence time window. The window width is then chosen to optimize the signal-to-noise ratio at each count rate level. To further evaluate the improvement we have also compared the BGO system to a BaF2 system.