Expressions for the various molecular contributions to the mean bending constant k(c) of a thermodynamically open vesicle bilayer have been derived, from which k(c) maybe calculated from an appropriate molecular-thermodynamic model as a function of the structure of the surfactants making up the aggregates as well as the solution state. It is demonstrated that k(c) determines the shape of a vesicle bilayer insofar as spherical vesicles form when k(c) is large and positive! whereas nonspherical. vesicles predominate at values of k(c) close to or below zero. It is found that contributions due to electrostatics and residual headgroup effects, which are present for one-component as well as mixed aggregates, mainly give rise to a positive value of k(c) whereas geometrical packing constraints are less important. However, the mixing of two or more surfactants can significantly reduce k(c) to values where nonspherical vesicles may begin to form. The magnitude of the reduction of k(c) due to mixing increases with increasing asymmetry with respect to headgroup cross-section area, charge number, and hydrocarbon tail volume between two surfactants in a binary surfactant mixture. The asymmetry is most pronounced for a binary mixture where the surfactant that carries the charge has the larger headgroup and the smaller tail. The reduction of k(c) due to mixing is, however, expected to be less than the corresponding effect for the bilayer bending constant of a spherical vesicle as a result of an additional positive contribution in the expression for the compositional contribution to k(c).