Statistical agencies utilize models to synthesize respondent-level data for release to the general public as an alternative to the actual data records. A Bayesian model synthesizer encodes privacy protection by employing a hierarchical prior construction that induces smoothing of the real data distribution. Agencies balance a trade-off between utility of the synthetic data versus disclosure risks and hold a specific target threshold for disclosure risk before releasing synthetic datasets. They introduce a pseudo posterior likelihood that exponentiates each contribution by an observation record-indexed weight in (0, 1), defined to be inversely proportional to the disclosure risk for that record in the synthetic data. The use of a vector of weights allows more precise downweighting of high-risk records in a fashion that better preserves utility as compared with using a scalar weight. This method is illustrated with an application to the Consumer Expenditure Survey of the U.S. Bureau of Labor Statistics.