Lipid bilayer vesicles with fluid/fluid phase coexistence are promising model systems for biological cell membranes. They permit the investigation of the mechanical properties of lipid membranes that are important for understanding mechanistic aspects of biological membrane function. Comparison of experimentally obtained vesicle shapes to mechanical membrane theories has enabled us to determine the values of line tension and mean-curvature bending stiffness of liquid-ordered and -disordered membranes. An additional important parameter that controls membrane geometry is the spontaneous curvature, driven, for example, by peripheral protein coats or asymmetric lipid composition. We examine to what extent effects of differing spontaneous curvature and Gauss curvature stiffness between coexisting fluid phases can be distinguished by membrane shape analysis. We find that the equilibrium neck geometries of dumbbell-shaped vesicles and the shapes of vesicles close to budding are very similar for vesicles that differ in spontaneous curvature or Gauss curvature stiffness differences. However, the two parameters have qualitatively different influence on discontinuous budding transitions. © EPLA, 2009.