This paper proposes a novel decentralized technique for efficient integration of flexible demand in the electricity market. The analysis focuses on price-responsive appliances that schedule their power consumption on the basis of a demand/price signal received by a central entity. Previous work has shown that, when the devices population is sufficiently large to be described as a continuum, it is possible to provide necessary and sufficient conditions for the existence of a Nash equilibrium (no device has unilateral interest in changing its scheduling when considering the resulting profile of aggregate demand). These results are now extended in order to achieve an equilibrium also when the mentioned conditions are violated. To this purpose, a time-varying proportional constraint (equal for all devices) is introduced on the power rate of the price-responsive appliances so as to limit the variation of flexible demand that they can introduce at critical time instants. The proposed design technique not only guarantees existence of a Nash equilibrium but it also minimizes the global operation time of the appliances population. Simulation results are provided and it is shown that, under the considered assumptions, each individual appliance completes its task in minimum time.