Low demand for index insurance in several recent pilot programs has created a puzzle for development economists and policy makers concerned with enhancing farmers risk management capacity in low-income economies. This paper contributes to the resolution of this puzzle by providing empirical evidence on the relative effectiveness of two primary frameworks for modeling decision-making under uncertainty. Specifically, we test whether features of Cumulative Prospect Theory (CPT), or Expected Utility Theory (EUT), better predict farmers' demand for crop insurance. Whereas in EUT, risk preferences can be represented by a single risk aversion parameter, in CPT they are determined by at least four components: probability weighting, the curvature of a utility function, a reference income and loss aversion. The data come from a series of unframed and framed lotteries played with 480 small-holder cotton farmers in southern Peru. The unframed risk games allow us to measure individual-specific preference parameters, for both theories. We use these parameters to generate predictions of farmers' choices in two framed insurance games in which farmers choose to purchase one of two available insurance contracts or to purchase no insurance. In the first game, farmers' earnings are framed as gross revenues and are always positive, i.e., this game is played over gains. In the second game, earnings are framed as net revenues and may be either positive or negative so that this is a game played over mixed prospects. We test the relative performance of the two theories by comparing the predictions of farmers' choices versus their actual choices in the insurance games. An important finding with respect to marketing of insurance contracts is that framing incomes as net revenues instead of gross revenues increases the CPT predicted demand by 24%. In the actual insurance games however, only 8% more farmers chose insurance in the net revenues frame. We find that neither theory is a particularly strong predictor of insurance choices, although EUT fares better than CPT for better educated farmers.