In the paper, the regulation of nonminimum systems using a nonlinear minimum-variance control strategy is considered. The relationship between output variance and control limit of a saturating actuator is investigated. Both ultimatum simulation studies and an approximate analysis based on the statistical linearisation of the nonlinearity are presented. The results of these studies demonstrate that a minimum exists on this relationship. The connection between the use of a nonlinear controller and a suboptimal linear control law is discussed.