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Noise measurements on CdZnTe detectors show that the main sources of detector-related noise are shot noise due to bulk leakage current and 1/f noise due to the detector surfaces. The magnitude of surface leakage current appears to have little or no effect on the detector noise. Measurements on guard-ring devices fabricated using gold-evaporated contacts show that the contacts behave as Schottky barriers and that the bulk current at typical operating voltages is in most cases dependent on the contact properties rather than directly on the material's bulk resistivity. This suggests that the level of shot noise can be controlled by changing the behavior of the contacts. A significant reduction in the noise of CdZnTe coplanar-grid detectors has been obtained using a modified contact fabrication process.