The problem considered is that of estimating simultaneously the differences between the means of p ≥ 2 test treatments and the mean of a control treatment. For design purposes the population variances of all p + 1 treatments are regarded as known. Tables are given that provide the experimenter with a basis for determining the minimal total number of experimental units and the optimal allocation of these units among the p + 1 treatments, in order to make one-sided or two-sided joint confidence interval estimates of the differences between the mean of each of the test treatments and the mean of the control treatment. These intervals achieve a specified joint confidence coefficient 1 - α for a specified allowance associated with the common width of the interval estimates. Comparisons with some competing allocation rules are also given.