Experimental conditions were investigated for growth of inclusion-free near-stoichiometric CdZnTe single crystals with a minimized concentration of native point defects. The positions of the stoichiometric line PS = 8×105exp (-1.76×104/T) (atm) and the room-temperature and high-temperature p-n lines were evaluated from high-temperature in situ galvanomagnetic measurements. The Cd pressure at the congruent melting point was estimated at ~1.15-1.20 atm from analysis of the total inclusion volume of five single crystals fabricated at Cd pressures in the range of 1-1.3 atm. An inclusion-free single crystal was prepared at PCd~1.2 atm. Calculations based on a model of two major defects, the Cd vacancy and the Cd interstitial, show that a very small deviation of PCd from PS results in a large generation of the native defects. Thus a reproducible production of a high-resistivity material by a slow cooling along the PS seems to be very difficult.