For the location parameter family of distributions $F(x - \theta)$ under some regularity conditions, a confidence interval for $\theta$ of fixed width $2d$ and given confidence coefficient $1 - \alpha$ in the limit as $d$ tends to zero is obtained using Hodges-Lehmann estimates based on Wilcoxon statistics. An upper bound on the average sample size is also given.
"On Sequential Confidence Intervals Based on Wilcoxon Type Estimates." Ann. Statist. 1 (6) 1200 - 1202, November, 1973. https://doi.org/10.1214/aos/1176342569