Full control over the density and emission properties of GaN quantum dots (QDs) should be feasible, provided that the growth proceeds in the Stranski-Krastanov (SK) growth mode. In this work, we derive the phase diagram for GaN QD formation on AlN by NH3-molecular beam epitaxy and analyze the corresponding optical signature by micro-photoluminescence (mu-PL). Interestingly, the growth window for SK-GaN QDs is very narrow due to the relatively small lattice mismatch of the GaN/AlN system (2.5%), constituting a fundamental challenge for QD growth control. By relying on bulk AlN single crystal substrates, we demonstrate QD density control over three orders of magnitude, from 10(8) to 10(11)cm(-2) by changing the growth rate. In contrast, the QD density is pinned to 2 x 10(10)cm(-2) when growing on AlN/sapphire templates, which exhibit dislocation densities on the order of 10(10)cm(-2). Thanks to QD densities as low as 10(8)cm(-2) on bulk AlN, we can probe the emission of spatially isolated single GaN QDs by mu-PL on unprocessed samples. (C) 2019 Author(s).