Index-based weather insurance has had low effective demand in spite of attractiveness of the product in avoiding moral hazard in insurance claims. We use a set of field experiments to assess willingness to pay for index insurance among coffee producers in Guatemala. We show that the probabilistic nature of the insurance is the main reason that makes it unappealing. This is due to a secular dislike of the presence of uninsurable risk that manifests itself even when the actual probability of contract non-performance is minimal, and is consistent with the overweighting of small probabilities in Prospect Theory. This implies that increasing the demand for index insurance needs modifying the product to cover multiple risks. This can be done by more effective indexing and/or by indexing outcomes such as yield instead of indexing the determinants of yields.