We demonstrate the existence of multiple dimensions of private information in the long-term care insurance market. Two types of people purchase insurance: individuals with private information that they are high risk and individuals with private information that they have strong taste for insurance. Ex post, the former are higher risk than insurance companies expect, while the latter are lower risk. In aggregate, those with more insurance are not higher risk. Our results demonstrate that insurance markets may suffer from asymmetric information even absent a positive correlation between insurance coverage and risk occurrence. The results also suggest a general test for asymmetric information.