The influence of shear on a lamellar phase in the system sodium dodecyl sulfate/decanol/water was investigated by combined rheo-small angle light scattering. Three different regions were detected and all could be characterized by different scattering patterns in depolarized and polarized light scattering. Flow alignment of anisotropic domains in flow direction was found at low and high shear rates. A viscosity maximum was observed at intermediate shear rates, and different anisotropic scattering patterns were detected in polarized and depolarized scattering. The data are interpreted by a shear-induced formation of vesicles which displayed a characteristic four-lobe pattern in depolarized scattering. A butterfly pattern observed in polarized scattering indicated the existence of concentration fluctuations along the flow direction, The transitions between the three regions were reversible, but the formation of vesicles was found only when the sample was sheared for a long time at appropriate shear rates. Complicated rheological properties as, e.g., shear thinning and shear thickening, were found as a consequence of the structural changes.