In present choice models, it is assumed that the composition of individuals' choice sets does not affect their utilities. Preferences and choice behaviour are assumed to be independent of context. The constraints that individuals face are not modeled explicitly in the residential choice literature. In this paper we aim to propose and demonstrate how discrete choice experiments and universal logit models may be used to estimate choice models that permit one to measure and test the effects of constraints on housing choice behaviour and residential preferences. In particular, we wish to test whether preferences of divorcees are invariant with differential access to housing-market segments. The empirical findings obtained in the present study of residential choices of divorcees generally support the idea that access to particular segments affects the preference for other segments differentially. Estimated attribute effects were in anticipated directions, although not all were significant. The choice model, including the effects representing access to particular housing-market segments, outperformed the multinomial logit model at conventional probability levels, and odds ratios were shown to change dramatically as a function of the constraints on residential choice behaviour.