We present plausible candidates for the global minimum structures of Al-N(+) (N = 46-62) cluster ions, determined by pseudopotential density functional theory static calculations under the spin-polarized generalized gradient approximation. Our calculations provide a first important step toward the rationalization of recent calorimetric experiments on the meltinglike transition of Al-N(+). Most clusters with N >= 48 clearly adopt fragments of the face-centered-cubic (fcc) crystalline lattice, although with significant distortions and a substantial proportion of defects in some cases. Another important driving force for stabilization comes from (111)-like surfaces, as the clusters often prefer to adopt less compact structures in order to keep the proportion of (100)-like surfaces at a minimum level. Al-46(+) and Al-47(+) adopt rather disordered structures instead. We find indications of enhanced stabilities for N = 51, 57, and 61 and of a substantial structural change between Al-55(+) and Al-56(+). These features correlate, albeit qualitatively, with the experimental observations.