The rectangular phase in the lyotropic system sodium decyl sulphate (SdS)-decanol-water was studied by H-2 NMR and small-angle X-ray scattering. To investigate the variation in unit cell dimensions, the shape of the ribbons, and molecular segregation within the ribbons with composition, nine samples were prepared. The aspect ratio of the ribbon cross section was found to be independent of composition, rho = 1.42 +/- 0.02, whereas the aspect ratio of the unit cell varied with composition, b/a = 2.7 - 3.0. In general, the molecular distribution of SdS and decanol is highly nonuniform; the decanol concentration is 2.5 to 3.0 times higher in the central lamellar region of the ribbons than in their curved edges, while SdS accumulates in the curved regions. On addition of SdS, a vertical compression of the unit cell occurs (a decreases and b remains unchanged). However, the absolute dimensions of the ribbons remain constant and the added SdS accumulates in the central lamellar region of the ribbons. Addition of decanol yields horizontal expansion of the unit cell (a decreases and b increases) and the absolute dimensions of the ribbon cross section increase slightly. The added decanol distributes evenly in the aggregate.