The main problem to be solved here may be described as follows: Let X1, X2, ··· be independent random variables, each with density fθ(x) = 1/θ over (0, θ) and zero elsewhere. It is desired to estimate the unknown parameter θ by an interval of length at most d units and with confidence at least 1 −α, for some specified d>0 and α in (0, 1). An exact solution and an asymptotic theory for a sequential procedure are given in Sections 1 and 2, respectively. The procedure proposed in this article satisfies an admissibility criterion which may be stated in terms of the maximum possible number of observations or, alternatively, the expected number of observations.