Sublimation growth of AlN crystals in a sandwich system is studied both theoretically and experimentally. Two types of Al sources are examined - AlN powder and liquid Al. Two-dimensional modeling is employed to understand the nature of the growth failure at a pressure lower than the critical one, predicted in a recent paper [A.S.Segal et al, J.Cryst.Growth 211 (2000) 68]. A relationship between the temperature and pressure is found providing maximum AlN growth rates.