The `back' transition from H-mode to L-mode has been studied on DIII-D as a part of our investigation of the L-H transition power threshold scaling. Based on a density-dependent scaling for the H-mode power threshold, ITER will require substantial hysteresis in this parameter to remain in H-mode as rises. Defining the hysteresis in terms of the ratio of sustaining to threshold power, may need to be as small as 50% for ITER. Operation of DIII-D at injection powers slightly above the H-mode threshold results in an oscillatory behaviour with multiple forward-backward transitions in the course of a discharge. These discharges represent a unique system for studying various control parameters that may influence the state transition. Careful analysis of the power flow through the edge gives values for the sustaining power well below the corresponding threshold powers , indicating that substantial hysteresis can be achieved in this parameter. Studies of other control parameter candidates such as the edge temperature during the back transitions are less clear: the amount of hysteresis seen in these parameters, if any, is primarily dependent on the nature (ELMing, ELM-free) of the parent H-state.