The optical signatures of Mg-related acceptors in GaN have been revisited in samples specifically grown on bulk GaN templates, to avoid strain broadening of the optical spectra. Bound-exciton spectra can be studied in these samples for Mg concentrations up to [Mg] approximately 2 x 10(19) cm(-3). Contrary to previous work it is found that instabilities in the photoluminescence spectra are not due to unstable shallow donors, but to unstable Mg-related acceptors. Our data show that there are two Mg-related acceptors simultaneously present: the regular (stable) substitutional Mg acceptor, and a complex acceptor which is unstable in p-GaN.