Better insurance against rainfall risk could improve the security of hundreds of millions of agricultural households around the world. However, customers have shown little demand for stand-alone insurance products. This paper theoretically and experimentally analyzes an innovative financial product called a Weather Insurance Savings Account (WISA), which combines savings and rainfall insurance. The paper uses a standard model of intertemporal insurance demand to study how customers demand for a WISA varies with the amount of insurance offered. A laboratory experiment is then used to elicit participants valuations of pure insurance, pure savings, and intermediate WISA types. Contrary to the standard model, within-subjects comparisons show that many participants prefer both pure insurance and pure savings to any interior mixture of the two, suggesting that market demand for a WISA is likely to be low. Additional experimental and observational evidence distinguishes between several alternative explanations. One possibility that survives the additional tests is diminishing sensitivity to losses, as in prospect theory.