A generalized (extreme Studentized deviate) ESD many-outlier procedure is given for detecting from 1 to k outliers in a data set. This procedure has an advantage over the original ESD many-outlier procedure (Rosner 1975) in that it controls the type I error both under the hypothesis of no outliers and under the alternative hypotheses of 1, 2, …. k-l outliers. A method is given for approximating percentiles for this procedure based on the t distribution. This method is shown to be adequately accurate using Monte Carlo simulation, for detecting up to 10 outliers in samples as small as 25. Tables are given for implementing this method for n = 25(1)50(10)100(50)500; k = 10, α = .05, .Ol, .005.