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Incomplete health insurance enrollment is a persistent U.S. challenge despite large subsidies. We ask whether hassles built into enrollment systems matter for insurance take-up and targeting. Studying removal of an auto-enrollment policy, we find that a small hassle – a requirement to actively select a health plan to enroll – reduces take-up by 33%, a major impact equivalent to $470 (57%) higher enrollee premiums. Hassles differentially screen out younger, healthier, and poorer people – groups with both low value and costs of insurance. We show that this value-cost correlation – a standard feature of insurance, where risk drives both – may undermine the classic rationale for ordeals' favorable targeting.