Discrete minimum variance controllers subject to a constraint on the variance of the manipulated variable, that is, constrained minimum variance (CMV) controllers, are shown to exhibit good performance and robustness properties. These CMV controllers are internal model controllers (IMC) for specified disturbance structures, and the Wiener-Hopf design procedure used to obtain them provides a convenient means of obtaining stable model inverses and filters. The higher order filters usually provided by this design approach give both good disturbance prediction and rapid gain roll-off at high frequencies. © 1987, American Chemical Society. All rights reserved.