The following criteria for determining best substitute interval estimators of a given class for a population parameter are considered in this paper: (1) minimizing the expected length of the confidence interval (maximizing the effectiveness); (2) minimizing the sum of the mean (absolute) deviations of the upper and lower confidence bounds from the true value (maximizing the effectivity); and (3) minimizing the sum of the mean squared deviations of the upper and lower confidence bounds from the true value (maximizing the efficiency). Modified forms of these criteria can also be applied to one-sided confidence intervals. Both theoretical and practical reasons are given for preferring criterion (3) to the others. A second main point of the paper is that exact confidence intervals, when available, are superior (and often far superior) to approximate ones. Both points are illustrated by a study of confidence bounds, based on one quasi-range, for the standard deviation of a normal population.