AbstractIn computer simulation experiments, when applying the method of control variates, it is useful to know the covariance matrix as well as the means of the control variates. Most control variates suggested in the literature are sample means whose true mean is known but whose covariance matrix is not. Such variates are shown not to be the best, and that by the use of standardised sums rather than sample means, control variates are obtained with known covariances as well as means. Linear combinations of these variates are shown to be best in that more complicated functions of these variates do not achieve additional increase in estimate accuracy. Numerical illustrations are given.