Molecular-beam-epitaxial (MBE) GaN layers can be made semi-insulating (SI) by using a high N flux during growth. For growth at low N flux, the samples have high concentrations (>10(18) cm(-3)) of shallow donors and shallow accepters, and also contain a deep center producing a yellow band (2.2 eV) in photoluminescence (PL). For growth at high N flux, the PL lines attributed to shallow accepters and the yellow band disappear, and the only remaining lines are due to the ground and excited states of the free-exciton A and B bands. The SI material does not produce a measurable Hall effect: and the conduction mechanism is assigned to hopping between deep defects. Using arguments from stoichiometry and theory, we tentatively assign the shallow donors, shallow accepters, and deep center to the N vacancy, Ga-antisite/Ga-vacancy complex, and Ga antisite, respectively. (C) 1997 Elsevier Science S.A.