We examine insurance markets with two-dimensional asymmetric information on risk type and on preferences related to regret. In contrast to Rothschild and Stiglitz (1976), the equilibrium can be efficient; that is, it can coincide with the equilibrium under full information. Furthermore, we show that pooling, semipooling, and separating equilibria can exist. Specifically, there exist separating equilibria that predict a positive correlation between the level of insurance coverage and risk type, as in the standard economic models of adverse selection, but there also exist separating equilibria that predict a negative correlation between the level of insurance coverage and risk type. Since optimal choice of regretful customers depends on foregone alternatives, the equilibrium includes a contract that is offered but not purchased.