This paper sheds new light on the forces that drive residential segregation on the basis of race, assessing the extent to which across-race differences in other household characteristics can explain a significant portion of observed racial segregation. The central contribution of the analysis is to provide a transparent new measurement framework for understanding segregation patterns. This framework allows researchers to characterize patterns of segregation, to decompose them in meaningful ways, and to carry out partial equilibrium counterfactuals that illuminate the contributions of a variety of non-race characteristics in driving segregation. We illustrate our approach using restricted micro-Census data from the San Francisco Bay Area that provide a rich joint distribution of household and neighborhood characteristics not previously available to the research community. In contrast to findings in the prior literature, our analysis indicates that individual household characteristics can explain a considerable fraction of segregation by race, explaining almost 95% of segregation for Hispanic, over 50% for Asian, and 30% for White and Black households.