Design principles for robust vesiculation. The rigidity of the plasma membrane, as well as the membrane tension, resists budding by curvature-generating coats. In the low tension regime, as defined by the vesiculation number, increasing the coat area or spontaneous curvature is sufficient to induce a smooth evolution from a flat membrane to a closed bud. A combination of increased coat rigidity and force from actin polymerization is necessary to ensure robust vesiculation in the high membrane-tension regime.