Can measured risk attitudes and associated structural models predict insurance demand? In an experiment (n = 1,730), we elicit measures of utility curvature, probability weighting, loss aversion, and preference for certainty and use them to parameterize seventeen common structural models (e.g., expected utility, cumulative prospect theory). Subjects also make twelve insurance choices over different loss probabilities and prices. The insurance choices show coherence and some correlation with various risk-attitude measures. Yet all the structural models predict insurance poorly, often less accurately than random predictions. Simpler prediction heuristics show more promise for predicting insurance choices across different conditions.