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The presence of Te inclusions degrades the quality of today's CdZnTe (CZT) crystals used for Xand gamma-ray detectors; both their sizes and concentrations densities must be reduced. Over the past years, many researchers proposed using long-term annealing (>;24 h) under Cd vapor pressure to reduce or even eliminate the inclusions visible under IR microscopes. We annealed detector-grade CZT samples for periods of 15 to 60 min under Cd-, Zn-, or Te-overpressure or in vacuum at 1000-1200 K. We determined the optimal temperature, duration, and the vapor atmosphere for such high-temperature annealing, typically at ~1100 K for 0.5-1.0 h. The results were very promising in eliminating Te-rich inclusions, even on twins where the inclusions are more stable than in the unperturbed lattice; indeed, we saw almost no inclusions whatsoever by IR transmission microscopy after such annealing. We note that eliminating inclusions at lower temperatures takes much longer. However, annealing under a Cd vapor pressure at temperatures above ~1170 K generates a large quantity of irregular Cd inclusions. The samples' resistance after annealing was estimated by I-V curves.