  We obtain a limit of a hierarchical Bayes estimator of a finite population
mean when the sample size is large. The limit is in the sense of ordinary
calculus, where the sample observations are treated as fixed quantities. Our
result suggests a simple way to correct the hierarchical Bayes estimator to
achieve design-consistency, a well-known property in the traditional
randomization approach to finite population sampling. We also suggest three
different measures of uncertainty of our proposed estimator.
