SUMMARY A simple procedure for producing confidence intervals of a desired width for the mean of a normal variable when the variance is unknown is presented, which amounts to repeatedly applying the usual fixed-sample interval procedure until the interval is of desired width, with the modification that the t confidence coefficient used for a given sample size n be based on n - 6 rather than n - 1 degrees of freedom. Numerical results presented show this procedure to be valid (to the nearest percent) for independent, identically distributed normal variables, regardless of the variance, specifically for confidence levels of 95 % and 99%, and it is argued that this same procedure may be expected to be valid for any level greater than or equal to 95 %. In addition, a result of Woodroofe is used to show that the procedure is asymptotically sample-size optimal as the specified interval width tends to zero, unlike the well-known two-stage procedure of Stein. The application of the method to group sequential trials is also discussed.