Equilibrium unilamellar vesicles are stabilized by one of two distinct mechanisms depending on the value of the bending constant. Helfrich undulations ensure that the interbilayer potential is always repulsive when the bending constant, K, is of order k BT. When K Ͼ Ͼ k BT, unilamellar vesicles are stabilized by the spontaneous curvature that picks out a particular vesicle radius; other radii are disfavored energetically. We present measurements of the bilayer elastic constant and the spontaneous curvature, R o, for three different systems of equilibrium vesicles by an analysis of the vesicle size distribution determined by cryo-transmission electron microscopy and smallangle neutron scattering. For cetyltrimethylammonium bromide (CTAB)͞sodium octyl sulfonate catanionic vesicles, K ‫؍‬ .7 k BT, suggesting that the unilamellar vesicles are stabilized by Helfrich-undulation repulsions. However, for CTAB and sodium perfluorooctanoate (FC7) vesicles, K ‫؍‬ 6 kBT, suggesting stabilization by the energetic costs of deviations from the spontaneous curvature. Adding electrolyte to the sodium perfluorooctanoate͞CTAB vesicles leads to vesicles with two bilayers; the attractive interactions between the bilayers can overcome the cost of small deviations from the spontaneous curvature to form two-layer vesicles, but larger deviations to form three and more layer vesicles are prohibited. Vesicles with a discrete numbers of bilayers at equilibrium are possible only for bilayers with a large bending modulus coupled with a spontaneous curvature.