One in five patients who get elective surgery at U.S. hospitals that accept their insurance may still get surprise medical bills, especially if they receive anesthesia, a new study suggests.

The study looked at what happened to almost 350,000 patients who had non-emergency surgery between 2012 and 2017 at hospitals and clinics that belonged to their health plan network, using surgeons who accepted their insurance.

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It’s not clear from the study exactly why patients received surprise bills or what they might do to avoid them, said Michelle Mello, a health policy researcher at Stanford University School of Medicine who wasn’t involved in the new research.

One thing patients can do, however, is think carefully about whether it makes sense for them to purchase what’s known as a “narrow network” plan, which might have lower premiums but a very limited number of in-network providers and steep fees for getting care outside the network, Mello said by email.

“While their premiums are affordable, there are countervailing costs: you may have to wait a lot longer to see a specialist, for example; and there’s a higher risk that the people who take care of you in the hospital won’t all be in network,” Mello said.

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People should also ask their surgeons, hospitals and insurance companies about out-of-network billing, Mello advised. Hospitals should be able to explain whether an elective surgery might involve out-of-network clinicians.

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“Make a stink,” Mello advised. “It’s often possible to negotiate these down.”