The derivatives with respect to hydrostatic pressure of the deep energy levels associated with substitutional point defects in GaAs are evaluated and are found to be considerably smaller than the corresponding derivative of the fundamental band-gap energy. A deep level can be driven out of the gap by pressure, depending on its site, symmetry, and nearness to a band edge. The pressure dependence can be used to identify the site of a defect and the symmetry of its deep levels. A combination of the energy of a deep level, its pressure dependence, a theory of deep-level energies (which need be no more accurate than 0.6 eV), and the present theory eliminates all but a few point defects as candidates for producing a given level. In GaAs, E 2 is assigned to an As vacancy, E 3 and E 4 are probably associated with defect complexes, and EL 2 is very likely caused by either substitutional oxygen on an As site or As on a Ga site. © 1982 The American Physical Society.