GaN dots have been grown on c-plane sapphire and (111) Si substrates by reactive molecular beam epitaxy. A new method involving two-dimensional growth followed by a controlled annealing during which dots were formed was employed. Due to localization and large dot density, relatively high luminescence efficiencies were obtained on both substrates. Single layer dots were used for AFM analysis whereas 30 layer dots were used for photoluminescence experiments. AIN layers, some too thick for mechanical interaction between stacks, and some thin enough for vertical coupling were used. Strong polarization effects lead to a sizeable red shift, which depends on the size of the dots.