Consider the regression model Yj = pxj+ej and the problem of constructing a confidence interval for liP with P E (O,p·) where p. > O. Uniformity down to P = 0 is a major difficulty. In fact any procedure based on a fixed sample size, will have either infinite Consider the regression model Yj = pxj+ej and the problem of constructing a confidence interval for liP with P E (O,p·) where p. > O. Uniformity down to P = 0 is a major difficulty. In fact any procedure based on a fixed sample size, will have either infinite expected width or zero confidence (Gleser and Hwang 1987), confidence being the infimum of the coverage probability. Sequential sampling is used to construct fixed-width intervals of the form where T is an integer valued stopping time, PT is the least squares estimator for P based on T observations and h is the half-length of the interval. Stopping times Tb are derived so that these intervals have coverage probabilities converging to a set value 'Y as h -+ O. This convergence is uniform down to P = O. Furthermore the predictors Xj may be chosen adaptively.[+][-]