Cationic surfactants with an erucyl (C-22, monounsaturated) tail display unusual phase behavior in aqueous solution as a function of temperature and added salt concentration. Low amounts of salts with binding counterions such as sodium tosylate (NaTos) lead to highly viscoelastic wormlike micellar solutions. With further addition of salt, the viscosity decreases, and the solutions cloud on heating (i.e., exhibit lower consolute phase behavior). The cloud-point temperature and the zero-shear viscosity eta(0) pass in parallel through minima as a function of NaTos concentration. Cloud-point behavior is seen over a wider range of salt concentrations in the case of sodium salicylate (NaSal), which has an even stronger binding counterion. In the case of a weakly binding salt (NaCl), phase transitions are observed only at much higher salt contents, and the phase behavior is predominantly of the upper consolute type. Light and neutron scattering data show evidence of critical concentration fluctuations near the cloud point. The phase behavior and patterns of variation of rheological properties can be attributed to micellar branching, in agreement with recent theories and cryo-TEM studies.