Two low-temperature photoluminescence lines in GaN, in the region of energies commonly interpreted as longitudinal optical-phonon replicas of free excitons, donor-bound excitons, or acceptor-bound excitons, are reinterpreted as acceptor-bound excitons (A0X’s) collapsing to n=2 and n=3 excited states, respectively, of the acceptors involved. Application of this model to two sets of A0X-related lines in hydride-vapor-phase-grown GaN gives acceptor energies of 85±1, and 115±1 meV, respectively. The existence of such shallow acceptor states, if confirmed, is of great technological importance.