This paper presents novel methodologies for efficient deployment of flexible demand. Large populations of price-responsive loads are coordinated through a price signal and a power constraint broadcast by a central entity. Such quantities are designed in order to minimise a global objective function (e.g. total generation costs) and ensure a one-step convergence to a stable solution, characterised as a Nash equilibrium. Conditions for the sought equilibrium are preliminarily expressed as monotonicity of demand profiles under reordered coordinates and then they are imposed as constraints of a global optimisation, whose solution is calculated numerically. To reduce the computational complexity of the problem in scenarios with high penetration of flexible demand, clustering of the appliances is introduced. The global properties of the final stable solution and its optimality with respect to the task times of the appliances are analysed both theoretically and through simulation results.