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We measured, in the 873-1173 K temperature range, the temperature- and Cd vapor-pressure-dependences of the free electron density in single CdTe(In) crystals with different In contents. Increasing the cooling rate of the crystals and/or decreasing the well-defined Cd vapor pressure reduced the free-electron density. We interpreted and modelled these phenomena and the crystal's high-temperature electrical properties within the framework of Kroger's point-defect theory. Our experiments demonstrated the possibility of controlling the free-electron density in CdTe(In) crystals by changing the cooling rate. We supplemented a point-defect structural study of CZT(In) crystals by low-temperature (80-420 K) electrical measurements. These findings allowed us to identify the nature of the point defects responsible for free-carrier scattering, which is an important parameter influencing the mutau-product value in detector-grade material.