Health plans that shift more up-front costs onto you are rapidly becoming the norm. But millennials don’t seem happy about taking on the risk, even in exchange for a lower price.

Millennials want their parents’ old health insurance plan. A new survey from Bankrate found that almost half of 18-to-29-year-olds prefer a health plan with a lower deductible and higher premiums—meaning millennials would rather pay more out of their paycheck every month and pay less when they go to the doctor. Compared to other age groups, millennials are the most likely to prefer plans with higher premiums.

That surprised Bankrate insurance analyst Doug Whiteman. “One would assume people in this age group were not likely to get sick, so they’d choose the cheapest possible plan just to get some insurance,” he says.

In theory, millennials are perfect candidates for high-deductible plans. The conventional wisdom is that since young and healthy people tend to have very low health-care costs, they should opt for a higher deductible and keep more of their paychecks.

If, for example, you go to the doctor only for free preventive care, switching from the average employer-sponsored traditional PPO plan to the average high-deductible health plan would save a single person $229 a year in premiums, according to the Kaiser Family Foundation’s 2014 data.

Millennials shopping in the new health insurance marketplace last year didn’t want the cheapest plans either. According to the Department of Health and Human Services, more than two-thirds of 18-to-34-year-olds chose silver plans, which have mid-level premiums and deductibles. Only 4% picked catastrophic plans, the ones with the lowest premiums and out-of-pocket limits of around $6,000.

Why are millennials choosing to pay more for health care? Turns out the “young invincibles” don’t feel so invincible after all, says Christina Postolowski, health policy manager at a youth advocacy group called—as it happens—Young Invincibles. “Millennials are risk-averse and concerned about their out-of-pocket costs if something happens to them,” Postolowski says.

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Jeffrey R. Ungvary President