Using five variants of the Asian Disease Problem, we dissected the risky-choice framing effect by requiring each participant to provide preference ratings for the full decision problem and also to provide attractiveness ratings for each of the component parts, i.e., the sure-thing option and the risky option. Consistent with previous research, more risky choices were made by respondents receiving negatively framed versions of the decision problems than by those receiving positively framed versions. However, different processes were evident for those scoring high and low on numeracy. Whereas the choices of the less numerate showed a large effect of frame above and beyond any influence of their evaluations of the separate options, the choices of the highly numerate were almost completely accounted for by their attractiveness ratings of the separate options. These results are consistent with an increased tendency of the highly numerate to integrate complex numeric information in the construction of their preferences and a tendency for the less numerate to respond more superficially to non-numeric sources of information.