We have determined the boundaries of the single-phase water-in-oil microemulsion region of a ternary system (tetraethylene glycol monododecyl ether-dodecane-water) in the oil-rich corner of the phase diagram, as a function of water content and temperature. We have investigated the structures of reverse micelles at temperatures between the lamellar (LC) phase transition and the two-phase separation. Characterization studies have been carried out by dynamic quasi-elastic light scattering and small-angle X-ray scattering as well as by viscosity measurements. It was found that a consistent interpretation of the experimental results requires the complementarity of the above techniques. At a constant water-to-surfactant molar ratio of 13.7, the emerging picture of the isotropic phase is that near the two-phase boundary micelles behave as slightly solvated spheres of 52-Angstrom radius. With decreasing temperature and as the LC transition is approached, prolate aggregates, displaying an asymmetry of 6 +/- 2 are formed and can be considered to be a progressive structural change on the way to lamellae. The physical properties of the system reported herein may have implications for the investigation of proteins in membrane-mimetic media.