Smallest confidence intervals for one binomial proportion

We specify three classes of one-sided and two-sided 1-α1-α confidence intervals with certain monotonicity and symmetry on the confidence limits for the probability of success, the parameter in a binomial distribution. For each class of one-sided confidence intervals the smallest interval, in the sense of the set inclusion, is obtained based on the direct analysis of coverage probability functions. A simple sufficient and necessary condition for the existence of the smallest two-sided confidence interval is provided and the smallest interval is derived if it exists. Thus the proposed intervals are uniformly most accurate, and have the uniformly minimum expected length as well.