We study the role of establishment-specific wage premiums in generating recent increases in West German wage inequality. Models with additive fixed effects for workers and establishments are fit in four sub-intervals spanning the period from 1985 to 2009. We show that these models provide a good approximation to the wage structure and can explain nearly all of the dramatic rise in West German wage inequality. Our estimates suggest that the increasing dispersion of West German wages has arisen from a combination of rising heterogeneity between workers, rising dispersion in the wage premiums at different establishments, and increasing assortativeness in the assignment of workers to plants. In contrast, the idiosyncratic job-match component of wage variation is small and stable over time. Decomposing changes in mean wages between different education groups, occupations, and industries, we find that increasing plant-level heterogeneity and rising assortativeness in the assignment of workers to establishments explain a large share of the rise in inequality along all three dimensions.