A systematic theoretical study of stoichiometric clusters (NaI)(n) up to n = 15 is performed using the ab initio perturbed-ion (PI) model. The structures obtained are compared to previous pair potential results, and observed differences between (NaI)(n) clusters and previous ab initio results for other alkali halide clusters are discussed. (NaI)(n) clusters with n up to 15 do not yet show a marked preference for geometries which are fragments of the bulk lattice. Instead, stacks of hexagonal rings or more open structures are obtained as ground structures in clusters with n = 3, 6, 7, 9, 10, 12, 13, and 15, indicating that convergence to bulk structure is not achieved yet at this size range. Low-lying isomers, which are fragments of the crystal lattice, exist, nevertheless, for those cases. The binding energies show that clusters with n = 4, 6, 9, and 12 molecules are specially stable. The binding energy has been decomposed in contributions which allow for an intuitive interpretation. Some electronic properties like ionization potentials and electronic energy levels are also studied.