Agricultural index insurance indemnifies a farmer against losses based on an index that is correlated with, but not identical to, her or his individual outcomes. In practice, the level of correlation may be modest, exposing insured farmers to residual, basis risk. In this article, we study the impact of basis risk on the demand for index insurance under risk and compound risk aversion. We simulate the impact of basis risk on the demand for index insurance by Malian cotton farmers using data from field experiments that reveal the distributions of risk and compound risk aversion. The analysis shows that compound risk aversion depresses demand for a conventional index insurance contract some 13 percentage points below what would be predicted based on risk aversion alone. We then analyze an innovative multiscale index insurance contract that reduces basis risk relative to conventional, single‐scale index insurance contract. Simulations indicate that demand for this multiscale contract would be some 40% higher than the demand for an equivalently priced conventional contract in the population of Malian cotton farmers. Finally, we report and discuss the actual uptake of a multiscale contract introduced in Mali.