Eukaryotic secretory proteins exit the endoplasmic reticulum (ER) via transport vesicles generated by the essential coat protein complex II (COPII) proteins. The outer coat complex, Sec13-Sec31, forms a scaffold that is thought to enforce curvature. By exploiting yeast bypass-of-sec-thirteen (bst) mutants, where Sec13p is dispensable, we probed the relationship between a compromised COPII coat and the cellular context in which it could still function. Genetic and biochemical analyses suggested that Sec13p was required to generate vesicles from membranes that contained asymmetrically distributed cargoes that were likely to confer opposing curvature. Thus, Sec13p may rigidify the COPII cage and increase its membrane-bending capacity; this function could be bypassed when a bst mutation renders the membrane more deformable.