Consumers do not always consider all feasible alternatives when making choices. Moreover, the subset they consider often varies from consumer to consumer. What can we infer about consumers’ preferences from their choices when we observe their feasible sets but not their heterogeneous consideration sets? We tackle this question in the context of consumer choice under risk. We build a procedure to conduct inference on a model of risk preferences that allows for unobserved heterogeneity in consumers’ consideration sets. In addition, our model allows for unobserved heterogeneity in preference type (EU and non-EU) and in preferences within a type. Importantly, we make no assumptions about how the households’ considerations sets are formed. We show that the model nevertheless is partially identified, and we estimate the model using data on households’ deductible choices in auto and home insurance, leveraging advances in random set theory to characterize sharp identification regions and construct confidence intervals. Lastly, we illustrate how one can use our approach to assess the welfare effects of a market intervention. Joint with Levon Barseghyan (Cornell University), Maura Coughlin (Cornell University), and Joshua C. Teitelbaum (Georgetown Law School).