This paper investigates corporate hedging under regret aversion. Regret-averse firms try to avoid deviations of their hedging policy from the ex post best policy, an intuitive consideration if one has to justify one's decisions afterward. The study presents a model of a firm that faces uncertain prices and seeks to hedge both profit risk and regret risk with derivatives. It characterizes optimal hedge positions and shows that regret aversion leads to stronger incentives to hedge downside price risk than standard expected utility theory. In the profit region of the price distribution, however, regret aversion reduces the hedging of price risk to avoid large regret in the case of increasing prices. The results show that regret aversion has a strong effect on the choice of the hedging instrument and provides a preference-based explanation for the use of options in corporate risk management.