With effectively improved spectral resolution and signal‐to‐noise ratio, PL features are well resolved in the Te‐ and Cd‐rich Cd0.96Zn0.04Te crystals and ascribed to the neutral donor‐bound exciton (D0X), acceptor‐bound exciton (A0X), A‐center, and deep donor–acceptor pair. A detailed analysis indicates that (i) Cd pressure annealing drives the Te inclusions to the surface region of the crystal, destroys the inclusions by excess Cd atoms, and releases abundant donor‐like and acceptor‐like impurities; (ii) the PL features of the deep energy levels at 1.30–1.55 eV originate in the A‐center consisting Cd vacancy and one type shallow donor, and the PL feature at 1.474 eV is the so‐called SA luminescence of a donor–acceptor transition between an A‐center and another shallow donor. A quantitative description of the recombination scheme is established, and by which the effects of the annealing are clarified.