Heterovalent CsPbBr3 doping with Bi results in a significant red shift of the optical absorption of both single-crystal and powdered samples. The results of low-temperature (3.6 K) photoluminescence studies of perovskite single crystals indicate that the position of the excitonic luminescence peak remains unaffected by Bi doping that, in turn, infers that the band gap of Bi-doped perovskite is not changed as well. The position and state density distribution of the valence band and Fermi level of single-crystal perovskites were determined by another direct method of ultraviolet photoelectron spectroscopy. The obtained results show that Bi3+ doping causes no changes in the valence band structure but an increase in the Fermi level by 0.6 eV. The summary of the obtained results directly demonstrates that the concept of the band-gap engineering in Bi3+-doped CsPbBr3 halide perovskite is not valid.