The problem of simultaneously estimating the pairwise differences of means of four independent normal populations with equal variances is considered. A statistical computing procedure involving a trivariate t density constructs the exact confidence intervals with simultaneous co verage probability equal to $1-alpha$. For equal sample sizes, the new procedure is the same as the Tukey studentized range procedure. With unequal sample sizes, in the sense of efficiency for confidence interval lengths and experimentwise error rates, the procedure is superior to the various generalized Tukey procedures.