The work describes the physical principles of the exhaustive photodepopulation spectroscopy. This method allows one to determine the energy distribution of gap states in insulating materials using the observation of optically-assisted electron removal from the gap states in incremental spectral windows. Examples of the inferred energy distributions of acceptor-type electron states in several high-k oxide insulators (Al₂O₃, HfO₂, Gd_xAl_2-xO₃) indicate that these are »1-2 eV broad. At the same time, no detectable density of donor states, expected to be present due to oxygen vacancies, is found in the studied oxides.