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Index insurance – in which payments are based on an index correlated with, but not identical to, individual losses – has been faced with an unexpectedly low uptake, despite its promise as a tool for poverty alleviation. This paper offers new insights into the behavioral impediments to the uptake of index insurance. We start from the observation that an index insurance contract appears to the farmer as a compound lottery, with uncertainty about individual production outcomes, as well as about the validity of the index as a reflection of individual losses. Adopting the smooth model of ambiguity aversion to this insurance problem, we show that in theory this compound lottery structure per se will dampen the demand for index insurance. Using framed field experiments with cotton farmers in Southern Mali, we elicited the coefficients of risk aversion and compound-risk aversion. The experimental results find that almost 60% of farmers are compound-risk averse, and that the distribution of compound-risk aversion is such that it would nearly cut in half the potential demand for the standard index insurance contracts. Our results highlight the importance of designing contracts with minimal basis risk under compound-risk aversion. Such a reduction in basis risk would not only enhance the value and productivity impacts of index insurance, but would also assure that the contracts are purchased and have their anticipated impacts.