We studied the effect of solubilization of a hydrocarbon (decane) into the ternary surfactant system tetradecyldimethylamine oxide (TDMAO)/1-hexanol/water. For not too high hexanol concentrations, i.e. before in the ternary system a conventional lamellar phase is formed, it is always possible to achieve an one-phase O/W microemulsion. For intermediate hexanol concentrations a vesicle phase is formed, which upon solubilization of decane is transformed into the microemulsion phase. This transition has been monitored by means of electrical conductivity and viscosity, The solubility of decane depends largely on the amount of cosurfactant (1-hexanol) present, and an increase of about a factor of 30 compared to the binary TDMAO system may be achieved. Close to the solubilization capacity the structure is always of the droplet type where the droplet radius increases linearly with the hydrocarbon content, SANS experiments in the shell contrast revealed that these droplets are fairly monodisperse, and analysis of the results also showed that the hexanol should mainly be located in the amphiphilic shell that surrounds the hydrocarbon core. Finally the structural parameters, radius R and polydispersity index p, and the macroscopic interfacial tension were compared to a microemulsion theory that relates these quantities to the elastic properties of the interfacial film. General agreement with these predictions has been found, and values for the elastic constants have been estimated.