The dark steady‐state I–U characteristics of CdSe single crystals of high resistivity are measured. The temperature dependence of the I–U characteristics is interpreted in terms of space‐charge‐limited currents (SCLC) with a single trap level. The parameters of levels located in a forbidden gap are determined by combining SCLC technique with thermally stimulated current and Hall mobility, μ, measurements. It was found that μ = μ(T) is determined by the scattering due to clusters of imperfections. Depending on the location of the Fermi level relative to a single trap level a steep current increase at the end of the square law region can be caused by trap filling or field ionization. The article goes further into restrictions imposed on SCLC by the field ionization of traps.