Small angle neutron scattering, SANS, has been used to investigate the structure of mixed ionic-nonionic surfactant micelles of SDS and C12E6. For solution compositions rich in C12E6, the evolution of micelle size with composition exhibits a pronounced maximum, in qualitative, agreement with the theoretical predictions of Shiloach and Blankschtein [Langmuir 1998, 14, 7166], but with some important quantitative differences which are discussed. The solubilization of the alkane, hexadecane, into the mixed surfactant micelle suppresses the micelle growth with changing solution composition. For micelles rich in C12E6, hexadecane is solubilized predominantly into the palisade layer of the micelles, favoring small spherical micelles. The micellar growth with changing solution composition arises from changes in the balance between the headgroup and steric contributions to the free energy of micellization, and the addition of alkane further alters that balance in favor of small spherical micelles.