This paper studies allocation of the housing market by means of discrete choice models with availability constraints. This approach arises when uncertainty about the availability of some alternatives is introduced within the conventional framework of discrete choice models. Availability constraints may exist, for instance, because of a lack of transparency in the market, limitations on the supply side, or rent control associated with centralized housing distribution. If households experience availability constraints, they may react by waiting until the desired alternative becomes available or by switching to a second best alternative. Both reactions affect the observed choice probabilities and have to be taken into account in econometric work. These implications of availability constraints are pointed out in this paper. An empirical application concerns the regulated rental part of the Dutch housing market. We find evidence for the presence of availability constraints and second best choices and conclude that an analysis based on conventional discrete choice models may lead to biased results.