The two-field (pressure/density) model for the L→H transition is extended and analyzed qualitatively. In its original form the model is ambiguous as to the location of the transition within the range of bistability of particle and thermal fluxes. Here, the model is regularized by including (i) hyperdiffusion, (ii) time dependence, and (iii) curvature of the pressure profile. The regularizations (i)-(ii) agree and indicate that the Maxwell rule for the forward and back transition applies, as opposed to the maximum flux forward and minimum flux backward transition rules (which yields hysteresis) as suggested previously. Regarding (i)-(ii), simple models suggest that for a pressure gradient driven electric field shear bifurcation, the basic scale of the pedestal is inexorably tied to the particle fueling depth, which normally is the neutral penetration depth. There is no hysteresis predicted by the local model of transport suppression. However, the effect of pressure profile curvature (iii) changes these results substantially. When it dominates, the curvature effect reduces the transition threshold to the lower end of the range of heating power, which falls within the phase coexistence region for both forward and back transitions. This softens the transition threshold requirements. In this limit, the model with pressure curvature also predicts transitions which occur in regimes of flat density and driven exclusively by the temperature gradient. This allows the pedestal to extend beyond the fueling depth, and also allows some decoupling of density and pressure profiles. In a parameter range where the pressure curvature is less important the transition occurs somewhere between the above two limits. © 2008 American Institute of Physics.