An isotropic, clear phase at high alcohol content is found in a system composed of calcium dodecyl sulfate, water, and an alcohol of medium chain length, like pentanol. hexanol, heptanol, or octanol. This phase is located in that region of the phase diagram in which L-3 phases are classically formed. Most ionic surfactants, however, only form sponge phases when the ionic charge of the surfactant molecules is sufficiently shielded by excess salt. At 5% surfactant and octanol as cosurfactant, the L-3 phase disappears if more than 5% of the calcium ions are substituted by sodium. Calcium dodecyl sulfate, in some aspects, behaves like a nonionic or double-chain surfactant. The phase discussed in this article is completely transparent, has low viscosity, and exhibits neither birefringence nor yield stress. Viscosity, electrical conductivity, and freeze-fracture electron microscopy indicate the sponge structure of the phase. In contrast to typical L-3 phases, small-angle neutron-scattering experiments show a peak the position of which is nearly unshifted compared with that of the neighboring lamellar phase.