The recent method of Serfling and Wackerly (1976) for constructing fixed-width confidence intervals for the center of location is extended to includeMestimators. The resultant class of procedures is compared to the stopping times of Chow and Robbins (1965), as both the interval lengthdand intended noncoverage probability 2α converge to zero. Except in certain special cases, the stopping times are found to have different asymptotic distributions. The coverage probability of the Serfling-Wackerly class is found asdconverges to zero.