In this paper we extend the independent availability logit and combined latent class mixed logit models to accommodate respondents with different consideration sets due to their cost thresholds and cut-offs. Pertinent features of our model are that it is estimated in WTP-space and that the class-specific WTP distributions are truncated to be within the bounds deduced from the cost level(s) within each class-specific consideration set. Our analysis shows that our approach is well suited at uncovering the heterogeneity in the cost thresholds and cut-offs used by respondents. This is shown to help build a richer insight into respondent׳s behaviour as well as raise a number of concerns about the appropriateness of assuming deterministic choice sets. We discuss the implications of our results for welfare analysis.