Optical characteristics of single-crystalline CdTe wafers are investigated. Their thermal annealing in the air brings about a wide luminescence band in the region of fundamental absorption (ħω > E g ), increase in the optical transmission factor T ω by more than one order of magnitude, as well as a shift of the high-energy edge T ω curve to 1.3 eV. These peculiarities are adequately explained in the framework of theory of quantum-size effects.