Mixtures of the phospholipid 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and the saponin beta-aescin spontaneously form monodisperse, bilayered discoidal micelles (also known as "bicelles" or "nanodisks") in aqueous solution. Such bicelles form below the melting temperature of DMPC when the phospholipids are in the rigid L-beta, state and are precursors of spontaneously formed vesicles. The aescin concentration must be far above the cmc(aescin) (approximate to 0.3-0.4 mM). It was found that the shape and size of the bicelles are tunable by composition. High amounts of aescin decrease the size of the bicelles from diameters of similar to 300 angstrom at 7 mol % to similar to 120 angstrom at 30 mol % beta-aescin. The structures are scrutinized by complementary small-angle X-ray and neutron scattering experiments. The scattering curves are subsequently analyzed by a model-independent (indirect Fourier transform analysis) and a model-based approach where bicelles are described as polydisperse bilayer disks encircled by a beta-aescin rim. Moreover, the monomodal distribution and low polydispersity of the samples were confirmed by photon correlation spectroscopy. The discoidal structures were visualized by transmission electron microscopy.