In a recent publication we compared phase behavior and scattering data obtained from SANS in water, n-alkane, n-alky 1 polyglycol ether (C iEj) mixtures. By analyzing the scattering spectra using the Teubner-Strey formula, it is possible to determine a measure for the amphiphilic strength of each system called the amphiphilicity factor, f a. It was demonstrated that the amphiphilicity factor is constant on a variety of surfaces within the three-dimensional space of composition and temperature. For instance, the Lifshitz surface, where fa=0, depends on composition and temperature and may be a precursor for the L α phase. Here we show that the same sequence exists in the binary system water/C4E1, where the surfaces become lines in the two-dimensional composition-temperature planes. Variations in amphiphile concentration and solution temperature allow one to reach almost the entire accessible amphiphilicity scale (∞>fa>-1) within this simple binary mixture. The occurrence of the Lifshitz surface at high C 4E1 concentrations and its disappearance as a function of temperature give more evidence that the Lifshitz region can be treated as a precursor of the lamellar liquid crystalline phase. While earlier investigations of water/C4E1 solutions in the dilute regime support the existence of micellar aggregates, the current work provides the first definitive evidence of the presence of supramolecular aggregates and short range order in the water/C4E1 system in the amphiphile-rich region.