Two procedures for treatment of outliers are considered for samples of normally distributed observations with known variance. The first procedure is a sequential adaptation of the usual maximum residual test for one outlier. If the maximum residual exceeds a predetermined constant, the largest observation is declared an outlier. In this event the test is repeated using the remaining observations. In the second procedure the two largest observations are declared outliers if the sum of the two largest residuals exceeds a predetermined constant. The performance of the two procedures is investigated for samples which contain two observations of mean higher than the common mean of the other observations. For the sequential procedure samples containing one high and one low outlier are also considered.