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It is demonstrated by in situ reflection-high-energy-electron-diffraction studies that the growth of hexagonal GaN on AlN occurs either purely in a layer-by-layer mode or in a Stranski-Krastanov mode, depending on the substrate temperature. Nanometric GaN islands embedded in AlN were fabricated by controlling the growth mode. Electron microscopy and atomic-force microscopy revealed that the dimensions of GaN dots could be varied down to values where zero-dimensional quantum effects are expected: the smallest dots were typically 10 nm wide and 2 nm high. These results open the way to the fabrication of quantum dots in materials with optical properties in the uv wavelength range.