We analyze how customers with limited attention value and choose among health plans. We show how the model can accommodate four observations regarding plan choice. First, people overweight the premium and thus underappreciate the value of health insurance. Second, insurance companies have a strong incentive to reduce quality and to hide these shortcomings in the fine print while attracting customers with insufficiently lower premiums. Third, customers may choose dominated alternatives. Finally, the willingness-to-pay for insurance is subadditive creating an incentive for providers to unbundle comprehensive plans. We discuss how these effects may result in a fundamental dilemma for policy makers.