We present ab initio perturbed ion calculations on the structures and relative stabilities of doubly charged [(NaCl)(m)(Na)(2)](2+) cluster ions. The obtained stabilities show excellent agreement with experimental abundances obtained from mass spectra. Those enhanced stabilities are found to be a consequence of highly compact structures that can be built only for certain values of m. Nearly all magic number clusters can be shown to be constructed in one of the two following ways: (a) by adding tri- or penta-atomic chains to two edges of a pet-feet neutral (NaCl)(n) cuboid, with n = m - 2 or n = m - 4, respectively, or (b) by removing a chloride anion from a perfect singly charged (NaCl)(n)Na+ cuboid, with n = m + 1.