The MAPbI₃ halide perovskite single crystals are studied at 5 K temperature using the photoluminescence excitation spectroscopy. Two noninteracting types of states are determined: bound excitons and defect-related states. Excitation of the crystal with light energy below the bound exciton resonance reveals the complex low-density defect emission, otherwise hidden by the emission of bound excitons. A way to separate these defect-related luminescence spectra is proposed, and the thorough study of this emission regime is carried out. The results of this study open an area of low-density defect and dopant exploration in halide perovskite semiconductors.