The reorganisation of nanocrystals in order to reduce their surface energies has been examined in computer simulations. The relaxation takes a qualitatively different path for sphalerite- and wurtzite-structured particles. The surfaces of the sphalerite particles reconstruct into hexagonal nets, but the interior remains identifiable as sphalerite-like, whereas wurtzite particles form facetted, hexagonal nanorods by virtue of a reorganisation of the whole particle which involves the creation of a low energy internal interface between oppositely oriented domains. Despite the reorganisation, the diffraction patterns remain compatible with a wurtzite structure with some internal strain. The dipole moments of thermalized wurtzite particles are compared with experimental results for CdSe.