We consider the problem of constructing confidence intervals of fixed width d and confidence level γ for the success probability p in Bernoulli trials. Algorithms are
given for calculating numerical lower bounds on the average expected sample size required and an asymptotic lower bound is obtained as d -> 0. Sequential and two-stage
procedures are proposed that attain the asymptotic lower bounds and nearly attain the numerical lower bounds. Asymptotically optimal sequential and two-stage
confidence intervals of fixed width and confidence level are proposed for the mean in a general (non-Bernoulli) context
