Methods for constructing simultaneous confidence intervals for all possible linear contrasts among several means of normally distributed variables have been given by Scheffé and Tukey. In this paper the possibility is considered of picking in advance a number (saym) of linear contrasts amongkmeans, and then estimating thesemlinear contrasts by confidence intervals based on a Studenttstatistic, in such a way that the overall confidence level for themintervals is greater than or equal to a preassigned value. It is found that for some values ofk, and formnot too large, intervals obtained in this way are shorter than those using theFdistribution or the Studentized range. When this is so, the experimenter may be willing to select the linear combinations in advance which he wishes to estimate in order to havemshorter intervals instead of an infinite number of longer intervals.