We study a health-insurance market where individuals are offered coverage against both medical expenditures and losses in income due to illness. Individuals vary in their level of innate ability and their probability of falling ill. If there is private information about the probability of illness and an individual's innate ability is sufficiently low, we find that competitive insurance contracts yield screening partly in the form of co-payment, i.e., a deductible in pay, and partly in the form of reduced medical treatment, i.e., a deductible in pain.