Versions of Cook’s (1977) D1 statistics are studied with reference to leverage and outliers in subset diagnostics. Exact dktributions are found under Gaussian errors; these typically are seen to be deficient in rank; and bounds for these are given in terms of standard distributions. It is shown that high leverage tends to mask effects of outliers resulting from a shift in mean or variance. This work corrects several common misconceptions regarding the use of D1 in regression diagnostics.