We derive the optimal structure of an insurance contract for regret averse policyholders. We show that the optimal contract always involves coinsurance, even if insurance is fairly priced. A deductible is optimal either if insurance is priced with a loading or if regret aversion dominates risk aversion. Put differently, deductibles can be optimal for fairly priced insurance contracts. Last, we show that regret aversion reduces the demand for insurance if insurance is fairly priced, whereas the effect of regret aversion on insurance demand is ambiguous if insurance is priced with high loadings.