Surveys are often designed with the purpose of producing reliable estimates at upper levels of aggregation, but information at disaggregated levels may also be needed. The demand for official statistics at fine levels and at low cost is motivating researchers to explore alternative estimation methods. For this work, the challenge originated with the U.S. Bureau of Labor Statistics’ National Compensation Survey (BLS’s NCS), which aims to collect wage and non-wage compensation data of employees in the United States. For this survey program, the BLS is interested in producing hundreds of thousands of employee compensation statistics that serve as key data in producing economic indicators, such as the quarterly Employment Cost Index and the Employer Costs for Employee Compensation, of interest especially to government agencies and institutions. In this paper, a bivariate hierarchical Bayes model is developed using sparse survey data available for fine domains defined by geography, occupations, work levels within occupations, and job characteristics (union/non-union membership, full-time/part-time work status, and incentive-based/time-based pay), from the NCS. Model predictions are then constructed for the small set of domains, for which survey data are available, and for a much larger set of domains, for which survey data are not available. Also, discussed in this paper are methods for addressing challenges in identifying the prediction space, in constructing and selecting the information that serves as model input, and in making use of relationships between variables and domains structure.