Many equilibrium microemulsion phases can solubilize hydrocarbon and water in all proportions in a continuous progression of states without any visibly abrupt transition. At the extremes are solutions of swollen micelles and swollen inverted micelles. Contending pictures of the midprogression microstructures are (1) crowded swollen micelles and crowded swollen inverted micelles, which cannot coexist alone, and (2) bicontinuous structures, parts of which can be micellar. Which is correct? The most extensive published evidence is electrical conductivity, small-angle x-ray scattering (SAXS), and viscosity data on microemulsions made in our laboratory with an alkylaryl sulfonate mixture that is a commercial type of surfactant. We report here complementary data with a comparable pure surfactant and analyze at length the SAXS evidence. We note that the pure surfactant appears to narrow the ranges over which swollen disjoint interacting micelles exist. We conclude that the continuous progression through buildup and breakdown of bicontinuous structures more readily explains all of our data and a number of findings by other investigators.