We examine a process of preparing oil-in-water nanoemulsions by quenching (diluting and cooling) precursor microemulsions made with nonionic surfactants and a cosurfactant. The precursor microemulsion structure is varied by changing the concentration of the cosurfactant. Water-continuous microemulsions produce initial nanoemulsion structures that are small and simple, mostly unilamellar vesicles, but microemulsions that are not water-continuous produce initial nanoemulsion structures that are larger and multilamellar. Examination of these structures by cryo-electron microscopy supports the hypothesis that they are initially vesicular structures formed via lamellar intermediate structures, and that if the lamellar structures are too well ordered they fail to produce small simple structures.