Douglas White knew high-deductible insurance is supposed to make patients feel the pain of medical prices and turn them into smart shoppers. So he shopped.

He called around for price quotes on the CT scan his doctor ordered. After all, his plan’s $2,000 deductible meant paying the full cost out of pocket. Using information from his insurer, he found a good deal — $473.53 at Coolidge Corner Imaging in Boston, a half hour from his house.

But the bill he got later was for $1,273.02 — more than twice as much — from a hospital he had no idea was connected to the imaging center.

“I was shocked,” said White, a doctor of physical therapy who thought he knew his way around the medical system. “If I get tripped up, the average consumer doesn’t have the slightest chance of effectively managing their health expenses.”

A national study by Consumers Union basically comes to the same conclusion, suggesting that there are millions of Douglas Whites lost in the medical billing maze.

Nearly one in three Americans with private health insurance surveyed by the research group got a surprise medical bill in the past two years — defined as when a plan paid less than expected and doctors and hospitals tried to recover the balance from the patient.

Of those with surprise bills, nearly a fourth got bills from doctors they had no idea were involved in their care and nearly two-thirds were charged more than they expected.

“When we talk about transparent health care and the need for consumers to shop around, it’s just not possible in many situations,” said Blake Hutson, a senior associate for Consumers Union, the policy arm of Consumer Reports. “Even if you work for a big company and have what you think is a good health insurance plan, you can get a surprise medical bill.”

The deductible is what patients pay before insurance kicks in. The higher the deductible, the more you pay out of pocket. Deductibles of $3,000 or $5,000 are not unusual these days, although the health law caps out-of-pocket costs at $6,600 for individuals and $13,200 for families.

Making plan members pay more in this way is supposed to prompt them to check prices and put competitive pressure on medical providers.

The problem is that you can’t buy medical services the way you buy a phone plan. Doctors, hospitals and other providers generally don’t advertise their prices and often keep them confidential, even when asked by patients about what to expect. Providers charge different amounts for the same service depending on the insurance.

One episode of treatment can generate bills from multiple caregivers, especially in the hospital.

A new study by the Employee Benefit Research Institute shows that members of high-deductible plans have higher incomes and are more educated on average than the typical American. But a post-grad degree from MIT might not be enough to figure out some bills.

The system is so complicated that one patient in three who got a surprise bill in the Consumers Union study didn’t investigate or fight it.

“I didn’t think it would make a difference,” or “I was confused about what to do” were common reasons for inaction.

That’s the wrong response, said Karen Pollitz, a senior fellow at the Kaiser Family Foundation who studies how the health system affects consumers. (Kaiser Health News is an editorially independent project of the foundation.)

“It’s always advisable to ask questions if you receive a surprise bill or if insurance pays less than you expect,” she said. “Mistakes happen and following up can save you money. If it gets too confusing or frustrating, ask for help.”

Consumers Union offers an online tool for finding the relevant agency in your state and its contact information.

White’s billing problems were cleared up — many months and phone calls later and after a reporter started inquiring.

His plan, Harvard Pilgrim Health Care, said it had given him an incorrect quote for the CT scan last fall. The plan eventually paid the imaging center the full $1,273, saying it wasn’t White’s fault that the plan’s quote was wrong.

The bill had come from Brigham and Women’s Hospital, which owned the radiology center, even though White said there was no indication of that when he went to get the scan.

Harvard Pilgrim said it didn’t know Brigham and Women’s was affiliated with the center, either. Hospital-owned facilities are often far more expensive than independently owned doctors’ offices.

So how does he like the transparency revolution in health care, boosting competition and empowering patients?

“There is nothing transparent about most health care billing,” White said.