We present a study of the phase behavior of quinary mixtures of water, salt, oils, alcohols, and single-tailed sodium n-alkyl sulfates, as it depends, in particular, on the carbon number of the alcohol, and that of the ionic amphiphile. We confirm that adding too much alcohol makes strongly structured mixtures become weakly structured so that the three-phase body may even disappear at a tricritical point. As with nonionic amphiphiles, this process is accompanied by a nonwetting --> wetting transition at the water/oil interface by the middle phase, and a gradual decrease of the conductivity change near the mean temperature of the three-phase body. A tricritical point may also-at least in principle-be approached by decreasing the carbon number of the ionic amphiphile, although an experimental verification is difficult due to the fact that the three-phase bodies drop out of the experimental window. The consequences of the results with respect to further research are briefly discussed.