A technique for designing moving-average precompensators that give the minimization of a tracking performance cost function while tracking either deterministic or stochastic reference inputs is presented. For deterministic reference inputs, the cost function is an infinite-time horizon quadratic sum of the dynamically weighted tracking error and dynamically weighted control input. For stochastic reference inputs, the sum of the variances of the dynamically weighted tracking error and dynamically weighted control input is minimized. The two types of cost function are shown to be equivalent and the same design technique is used for both. The precompensator is intended to be designed for use in cascade with a control system which has already been designed, possibly without regard to tracking. The minimization of the cost function is enhanced by increasing the number of terms in the precompensator above the minimum necessary to keep the cost finite. A simulation example is presented showing how performance improvements over pole-placement and error transfer function zero-placement controllers may be achieved.