We investigate the origin of the local curvatures of the interatomic surfaces of the theory of atoms in molecules. The analytic expressions obtained in a previous work are used as a basic guide to this end, and several simplified models of the electron density between a pair of interacting atoms demonstrate that the stiffness difference in the atomic densities near the bond critical points controls their signs and magnitudes. Some steps toward a systematic evaluation of the curvatures of simple molecules have also been taken, and a number of correlations between these curvatures and chemically relevant atomic properties are presented. (C) 2003 American Institute of Physics.