The utility of Bayes and empirical Bayes techniques is illustrated on an important problem often encountered in small area estimation. We propose various Bayes as well as classical James-Stein estimators, in order to correct the raw adjustment factors obtained from the Canadian Reverse Record Check and the Overcoverage Study in the 1991 Canadian Census Undercount. The James-Stein and the purely Bayes approach require good prior estimates. The hierarchical and empirical Bayes estimators, chosen to be particularly robust against partial prior misspecification, allow the data to determine the direction and the amount of shrinkage, and should be used when prior information is lacking.