The expected length of a confidence interval is shown to equal the integral over false values of the probability each false value is included. Thus two desiderata for choosing among confidence procedures lead to the same measure of desirability. Furthermore, by common definitions of “optimum,” a procedure is optimum as regards including false values if and only if it is optimum as regards expected length. However, the procedure with minimum expected length ordinarily depends on the true value of the parameter. The possibility is explored of minimizing the average expected length, averaging according to some weighting on the possible parameter values. (This is not the same as assuming a prior distribution and using Bayes' Theorem.) The ideas are applied to the mean and variance of a normal distribution and the probability of success in binomial trials.