Coefficients, variances and efficiencies are provided for the best linear unbiased estimates (BLUE's) of the mean and standard deviation of the logistic distribution, with both unknown, based on four order statistics with ranks giving the maximum joint efficiency among all BLUE's based on four order statistics. Asymptotic joint efficiencies are compared for asymptotically best linear estimates (ABLE's) based on order statistics with ranks determined by various spacings. With one parameter known, the BLUE's and ABLE's, using order statistics with ranks determined by the optimum spacings of the ABLE's, have efficiencies close to those of BLUE's based on optimum ranks.