The impact of two model perfumes with differing degrees of hydrophobicity/hydrophilicity, linalool (LL) and phenylethanol (PE), on the solution structure of anionic surfactant sodium dodecyl 6-benzene sulfonate, LAS-6, has been studied by small angle neutron scattering, SANS. For both types of perfume molecules, complex phase behavior is observed. The phase behavior depends upon the concentration, surfactant/perfume composition, and type of perfume. The more hydrophilic perfume PE promotes the formation of more highly curved structures. At relatively low surfactant concentrations, small globular micelles, L-1, are formed. These become perfume droplets, L-sm, stabilized by the surfactant at much higher perfume solution compositions. At higher surfactant concentrations, the tendency of LAS-6 to form more planar structures is evident. The more hydrophobic linalool promotes the formation of more planar structures. Combined with the greater tendency of LAS-6 to form planar structures, this results in the planar structures dominating the phase behavior for the LAS-6/linalool mixtures. For the LAS-6/linalool mixture, the self-assembly is in the form of micelles only at the lowest surfactant and perfume concentrations. Over most of the concentration-composition space explored, the structures are predominantly lamellar, L-w, or vesicle, L-v, or in the form of a lamellar/micellar coexistence. At low and intermediate amounts of LL, a significantly different structure is observed, and the aggregates are in the form of small, relatively monodisperse vesicles (i.e., nanovesicles), L-sv.