The presence of Te secondary-phase defects (i.e., Te inclusions and Te precipitates) is a major factor limiting the performance of CdZnTe (CZT) X-and gammaray radiation detectors. We find that Te secondary-phase defects in CZT crystals can be removed through post-growth, two-step annealing without creating new trapping centers (i.e., prismatic punching defects). Two-step annealing (with the first in a Cd pressure and the second one in a Te pressure) was demonstrated to be effective in removing the Te secondary-phase defects, while preserving the electrical resistivity of the CZT detector.The first step involves annealing of semi-insulating CZT under a Cd overpressure at 700/600 (CZT/Cd) for 24 hours, which completely eliminated the Te-rich secondaryphase defects (Te inclusions). However, it resulted in a lower resistivity of the samples (down to 2 × 10 4-6 Ω•cm). A subsequent annealing step involves processing CZT under a Te ambient condition at 540/380 (CZT/Te) for 120 hours, which restored the crystal's resistivity to 6.4 × 10 10 Ω•cm without creating new Te secondary-phase defects. However, Te inclusions reappeared in the case of unnecessarily long Te ambient annealing. Pulse height spectra taken with the two-step annealed CZT detectors showed improved detector performance due to a reduced concentration and size of Te secondary-phase defects. Index Terms-CdZnTe, two-step annealing, high resistivity, real-time monitoring, pulse height spectra I.