Taking as our point of departure a model proposed by David Card (2001), we suggest new methods for analyzing wage dispersion in a partially unionized labor market. Card's method disaggregates the labor population into skill categories, which procedure entails some loss of information. Accordingly, we develop a model in which each worker individually is assigned a union-membership probability and predicted union and nonunion wages. The model yields a natural three-way decomposition of variance. The decomposition permits counterfactual analysis, using concepts and techniques from the theory of factorial experimental design. We examine causes of the increase in U.K. wage dispersion between 1983 and 1995. Of the factors initially considered, the most influential was a change in the structure of remuneration inside both the union and nonunion sectors. Next in importance was the decrease in union membership. Finally, exogenous changes in labor force characteristics had, for most groups considered, only a small negative effect. We supplement this preliminary three-factorial analysis with a five-factorial analysis that allows us to examine effects from the wage-equation parameters in greater detail.