We reported previously the effects of both osmotic and curvature stress on fusion between poly(ethylene glycol)-aggregated vesicles. In this article, we analyze the energetics of fusion of vesicles of different curvature, paying particular attention to the effects of osmotic stress on small, highly curved vesicles of 26 nm diameter, composed of lipids with negative intrinsic curvature. Our calculations show that high positive curvature of the outer monolayer "charges" these vesicles with excess bending energy, which then releases during stalk expansion (increase of the stalk radius, r(s)) and thus "drives" fusion. Calculations based on the known mechanical properties of lipid assemblies suggest that the free energy of "void" formation as well as membrane-bending free energy dominate the evolution of a stalk to an extended transmembrane contact. The free-energy profile of stalk expansion (free energy versus r(s)) clearly shows the presence of two metastable intermediates (intermediate 1 at r(s) approximately 0 - 1.0 nm and intermediate 2 at r(s) approximately 2.5 - 3.0 nm). Applying osmotic gradients of +/-5 atm, when assuming a fixed trans-bilayer lipid mass distribution, did not significantly change the free-energy profile. However, inclusion in the model of an additional degree of freedom, the ability of lipids to move into and out of the "void", made the free-energy profile strongly dependent on the osmotic gradient. Vesicle expansion increased the energy barrier between intermediates by approximately 4 kT and the absolute value of the barrier by approximately 7 kT, whereas compression decreased it by nearly the same extent. Since these calculations, which are based on the stalk hypothesis, correctly predict the effects of both membrane curvature and osmotic stress, they support the stalk hypothesis for the mechanism of membrane fusion and suggest that both forms of stress alter the final stages, rather than the initial step, of the fusion process, as previously suggested.