Broad, low temperature photoluminescence (PL) peaks near 3.4–3.42 eV in GaN have previously been associated with basal-plane stacking faults. Recently, we observed unusually sharp and highly structured PL peaks in this region in high quality bulk GaN grown from a Na/Ga flux, some of which display characteristic shifts and narrowing as a function of excitation power. Here, we study these peaks as a function of excitation intensity and crystal polarity, and compare them to those observed in GaN grown on off-axis SiC or sapphire (0001) substrates by metalorganic chemical vapor deposition (MOCVD). In the off-axis material on either substrate, similar peaks are observed to those in the bulk samples. In addition, a low energy peak near 3.21 eV is observed, which does not occur in the bulk material.