The paper presents a method of designing digital controllers for randomly disturbed single-input/single-output linear systems with time delay which minimise the cost functionE{y2t+k+λu2t}. The process and noise models used are those obtained from current identification programs, and the control law developed has significant advantages over standard minimum-variance designs. (a) There is no difficulty with nonminimum-phase systems. (b) For processes with constraints on control effort, a marked improvement in the resultant output variance can be achieved. (c) There is a flexibility in the design to deal with cases where the closed-loop performance becomes unsatisfactory because of parameter drift or other causes. A typical example of the design procedure is given, and a comparison between the new control law and a minimum-variance law is made.