The 1990 census and Post-Enumeration Survey produced census and dual system estimates (DSE) of population by domain, together with an estimated sampling covariance matrix of the DSE. Estimates of the bias of the DSE were derived from various PES evaluation programs. Of the three sources, the unadjusted census is the least variable but is believed to be the most biased, the DSE is less biased but more variable, and the bias estimates may be regarded as unbiased but are the most variable. This article addresses methods for combining the census, the DSE, and bias estimates obtained from the evaluation programs to produce accurate estimates of population shares, as measured by weighted squared- or absolute-error loss functions applied to estimated population shares of domains. Several procedures are reviewed that choose between the census and the DSE using the bias evaluation data or that average the two with weights that are constant across domains. A multivariate hierarchical Bayes model is proposed for the joint distribution of the undercount rates and the biases of the DSE in the various domains. The specification of the model is sufficiently flexible to incorporate prior information on factors likely to be associated with undercount and bias. When combined with data on undercount and bias estimates, the model yields posterior distributions for the true population shares of each domain. The performance of the estimators was compared through an extensive series of simulations. The hierarchical Bayes procedures are shown to outperform the other estimators over a wide range of conditions and to be robust against misspecification of the models. The various composite estimators, applied to preliminary data from the 1990 Census and evaluation programs, yield similar results that are closer to the DSE than to the census. Analysis of a revised data set yields qualitatively similar estimates but shows that the revised post-stratification improves on the original one.