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Monte Carlo simulations of pulse height spectra for Cd1-xZnxTe detectors are used to investigate the effect of variations in alloy composition and carrier drift lengths on energy resolution. The results, which are based on a simple phenomenological model, show that these nonuniformities can have significant detrimental effects on spectrometer performance. For the case of Bridgman-grown material, the orientation of the growth axis relative to the detector axis is shown to be an important consideration, especially for crystals which come from the heel end of a boule, where the composition gradient due to zinc segregation is large. Other effects which we have simulated include growth striations, zinc segregation at grain boundaries, and trapping by inclusions and grain boundaries; each of these effects is detrimental to energy resolution. We conclude that material nonuniformity is a major obstacle to achieving statistically limited energy resolution in cadmium zinc telluride detectors.