Vesicle shape transformations caused by decreasing the difference between the equilibrium areas of membrane monolayers were studied on phospholipid vesicles with small volume to membrane area ratios. Slow transformations of the vesicle shape were induced by lowering of the concentration of lipid monomers in the solution outside the vesicle. The complete sequence of shapes consisted of a string of pearls, and wormlike, starfish, discocyte and stomatocyte shapes. The transformation from discocyte to stomatocyte vesicle shapes was analyzed theoretically to see whether these observations accord with the area difference elasticity (ADE) model. The membrane shape equation and boundary conditions were derived for axisymmetrical shapes for low volume vesicles, part of whose membranes are in contact. Calculated shapes were arranged into a phase diagram. The theory predicts that the transition between discocyte and stomatocyte shapes is discontinuous for relatively high volumes and continuous for low volumes. The calculated shape sequences matched well with the observed ones. By assuming a linear decrease of the equilibrium area difference with time, the ratio between the nonlocal and local bending constants is in agreement with reported values.