Just because you have health insurance doesn’t necessarily mean you can afford all your medical bills, especially if you have a high deductible. So sometimes, it pays to negotiate.

A Commonwealth Fund study released this week found that nearly a quarter of working-age Americans who had health insurance in 2014 were “underinsured.” The report cited rising deductibles — the amount you must pay for care before insurance coverage begins — as a growing factor.

More people than ever before have health plans with deductibles, the report found, and more people have deductibles that are high relative to their incomes. Half of those who were underinsured reported problems paying medical bills or said they were paying off medical debt, the report found.

High deductibles squeeze many families because most Americans lack significant savings to help cover sizable bills. “Most Americans don’t have that much money in the bank,” said Karen Pollitz, a health policy expert with the Kaiser Family Foundation.

So consumers may be interested to know that the amount of a medical bill is not necessarily set in stone, said Erin Singleton, chief of mission delivery for the Patient Advocate Foundation, which assists people with chronic conditions. You can ask whether a discount can be applied, or whether the hospital has funds available for patients with a financial hardship.

Often, people are embarrassed to talk to professionals about discounting their bills, said Martin B. Rosen, a co-founder of Health Advocate, which helps patients with employer-based coverage. But, he said, “There’s no harm in asking” — just be polite.

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Jeffrey R. Ungvary President