Best exact nonparametric confidence intervals for quantiles

Well-known nonparametric confidence intervals for quantiles are of the form (X-i:n, X-j:n) with suitably chosen order statistics X-i:n and X-j:n, but typically their coverage levels differ from those prescribed. It appears that the coverage level of the confidence interval of the form (X-i:n, X-j:n) with random indices I and J can be rendered equal, exactly to any predetermined level gamma epsilon (0, 1). Best in the sense of minimum E(J - I), i.e., 'the shortest', two-sided confidence intervals are constructed. If no twosided confidence interval exists for a given gamma, the most accurate one-sided confidence intervals are constructed.