In this paper, tenure choice in complex housing markets is examined, that is, in markets with more than a simple choice between own and rent. The paper has both substantive and technical foci. The substantive focus is to extend the authors' research on the links between housing and mobility and to provide detailed information on the way in which dwelling choices are made after the decision to relocate. The technical focus is to continue the authors' concern with building robust models of urban processes. The technical concerns are focused on special forms of automatic interaction detection and dummy variable multiple regression to estimate the influence of household characteristics and previous housing situation on dwelling choice. The data used in the analysis are part of a large sample taken in 1981 of all Dutch households. The automatic interaction detection method is used as a form of exploratory data analysis to identify the underlying `structure' in the data. The results are used as input to the dummy regression process, which, in combination with the proportional reduction in uncertainty measures, establishing the importance of income and the role of regional variations, age, and type of house as major predictors of tenure choice. A main conclusion from the research is that, even though income is the most important predictor, age, size of family, type of house, and price also affect tenure choice. Even more important is the conclusion that it is essential to do separate analyses for separate tenures.