The rheology of the shear-thickened state is investigated in low-concentration solutions of wormlike micellar solutions using mechanical, optical, and velocity profile measurements. The zero-shear-rate viscosity of the solutions increases by more than a factor of 1000 as the concentration of surfactant is increased from 1 to 10 mM. By contrast, the apparent viscosity of the shear-thickened state of these same solutions is observed to be remarkably independent of concentration over a wide range of shear rates. This is shown to be a consequence of the development of slip layers between the very viscous gellike shear-induced structures (SISs) which form in the bulk of the surfactant solution and on the walls of the Couette devices in which the measurements ar made. As the applied shear stress is increased even further, there is evidence that the SIS fractures give rise to shear-rate-independent stress and an apparent viscosity, which decreases with increasing shear rate. After the SIS fractures, large fluctuations in the shear rate are observed to result from an SIS which alternately fractures, slips, heals, and refractures. The fracture stress is proportional to the concentration and inversely proportional to the cell radius.