In recent experiments on sodium chloride clusters, structural transitions between nanocrystals with different cuboidal shapes were detected. Here we determine reaction pathways between the low-energy isomers of one of these clusters, (NaCl)35Cl –. The key process in these structural transitions is a highly cooperative rearrangement in which two parts of the nanocrystal slip past one another on a {110} plane in a (left-angle)1[overaccent (overbar) [above] 1]0(right-angle) direction. In this way the nanocrystals can plastically deform, in contrast to the brittle behavior of bulk sodium chloride crystals at the same temperatures; the nanocrystals have mechanical properties which are a unique feature of their finite size. We also report and compare the global potential-energy minima for (NaCl)NCl – using two empirical potentials, and comment on the effect of polarization.