E. Brandstatter, G. Gigerenzer, and R. Hertwig (2006) contended that their priority heuristic, a type of lexicographic semiorder model, is more accurate than cumulative prospect theory (CPT) or transfer of attention exchange (TAX) models in describing risky decisions. However, there are 4 problems with their argument. First, their heuristic is not descriptive of certain data that they did not review. Second, their analysis relied on a global index of fit, percentage of correct predictions of the modal choice. Such analyses can lead to wrong conclusions when parameters are not properly estimated from the data. When parameters are estimated from the data, CPT and TAX fit the D. Kahneman and A. Tversky (1979) data perfectly. Reanalysis shows that TAX and CPT do as well as the priority heuristic for 2 of the data sets reviewed and outperform the priority heuristic for the other 3. Third, when 2 of these sets of data are reexamined, the priority heuristic is seen to make systematic violations. Fourth, new critical implications have been devised for testing the family of lexicographic semiorders including the priority heuristic; new results with these critical tests show systematic evidence against lexicographic semiorder models.