A well-known method of designing control systems which are linear except for control signal saturation is to replace the saturation constraint by a constraint on the integral-square-value of the control signal, and then use lineal1 theory to calculate a controller which minimizes integral-square-error. In the present paper, this controller is compared with the best non linear controller, with a best linear controller which is such that the control signal only just leaches saturation and with the best linearly switched relay system. Three simple plants are considered. For these it is found that the energy-constrained design yields an integral-square-error which is up to 50% greater than the minimum obtainable, and yields controller parameters which differ from their optimal values by factors which can be large.