Why is there a general reluctance to buy insurance for low-probability-high-consequence risks and a preference for high-probability-low-consequence risk coverages? Using a regret-theoretical expected utility framework, we aim to shed light on such behavior. Regret theory posits not only that decision-makers experience regret following an ex-post “wrong” decision, but also that their anticipation of potential regret is integrated into their decision-making processes. Under regret, some risks are more regretful than others because the impact of regret aversion mainly kicks in at the extremes and so individuals will adjust optimal coverage accordingly. The often discussed failure of catastrophe insurance markets may be a consequence of this phenomenon.