Regression analysis in comparative research suffers from two distinct problems of statistical inference. First, because the data constitute all the available observations from a population, conventional inference based on the long-run behavior of a repeatable data mechanism is not appropriate. Second, the small and collinear data sets of comparative research yield imprecise estimates of the effects of explanatory variables. We describe a Bayesian approach to statistical inference that provides a unified solution to these two problems. This approach is illustrated in a comparative analysis of unionization.