We describe the numerical methods needed to obtain the desired posterior moments. Then we compare estimates produced using the exact numerical method with approximations. Finally, we compare the hierarchical Bayes estimates with empirical Bayes estimates and with standard methods, that is, synthetic estimates and estimates obtained from a conventional randomization-based approach. We use a cross-validation exercise to assess the quality of model fit. We also summarize the results of a separate study of the binary indicator of partial work limitation. Because we know the value of this variable for each respondent to the 1990 Census long form, we can compare estimates corresponding to alternative methods and models with very accurate estimates of the true values.