The conditions required for a high growth rate of AlN in a 3 × 2″ showerhead-type vertical flow metalorganic vapor phase epitaxy (MOVPE) reactor are studied. It is found that at the standard growth conditions (low V/III, 50 mbar, 1110 °C, H2), the growth rate linearly increases with the trimethylaluminium (TMAl) flow rate until about 280 μmol min−1 with some drop of precursor utilization efficiency at higher pressures. While the pre-reaction of TMAl with NH3 at 140 μmol min−1 of TMAl is still not a major issue, it is not possible, however, to maintain a smooth AlN surface morphology during this “fast” growth. To suppress the surface morphology deterioration, the growth pressure requires optimization. An increase of the growth pressure, to 75 mbar, is found to be critical to grow 20+ μm of smooth AlN at a rate of about 3.6 μm h−1 on bulk AlN substrates.