The periodic cluster model, a theoretical scheme recently developed in our laboratory, has been used, together with an atomistic pair potential energy model, to simulate AlN nanocrystals. The main advantages of this approach are a greatly reduced dimensionality and the ability to incorporate external pressure effects at the cost of neglecting geometric surface relaxation. The results suggest that small-size nanocrystals display graphitic-like layers, nonbuckled, as opposed to the buckled bulk wurtzite structure; buckling will dominate after a given, quite large, threshold. The surface tension, c/a ratio, and equation of state are examined with respect to variations on both pressure and nanocrystal size. It is found that, although the bulk modulus of the wurtzite-like phase is smaller (although decreasing with size) in nanocrystals than in the bulk, the nonbuckled phase displays a larger modulus, in agreement with the experiments. The transition pressure into the rocksalt-like phase increases with system size, with the dependence being linear against 1/N1/3. This is rationalized through a qualitative small-systems thermodynamical model.