WASHINGTON — Medicare’s prescription-coverage gap is getting noticeably smaller and easier to manage this year for millions of older and disabled people with high drug costs.

The “doughnut hole,” an anxiety-inducing catch in an otherwise popular benefit, will shrink about 40 percent for those unlucky enough to land in it, according to new Medicare figures provided in response to a request from The Associated Press.

The average beneficiary who falls into the coverage gap would have spent $1,504 this year on prescriptions. But thanks to discounts and other provisions in President Barack Obama’s health care overhaul law, that cost fell to $901, according to Medicare’s Office of the Actuary, which handles economic estimates.

A 50 percent discount that the law secured from pharmaceutical companies on brand-name drugs yielded an average savings of $581. Medicare also picked up more of the cost of generic drugs, saving $22.

Concern over cutting Medicare to expand coverage for the uninsured helped push older voters toward Republicans in the 2010 congressional elections. Obama and the Democrats have been trying to woo them back ever since.

“For people with high drug expenditures, the 50 percent discount offers real savings,” said Tricia Neuman, director of Medicare policy for the nonpartisan Kaiser Family Foundation. “It’s certainly more helpful than no coverage at all, which is what they had previously.”

More than 2 million beneficiaries already have gotten some help, discounts that have gone largely to middle-class seniors because the poor are covered in the gap at taxpayers’ expense.

For retired elementary school teacher Carolyn Friedman, it meant she didn’t need a loan to pay for drugs that keep her epilepsy under control.

“What a change for the better,” said Friedman, 71, of Sunrise, Fla. “This year, it was easier to pay my bills, whereas last year I had to borrow money to pay for my medications when I was in the doughnut hole.”

One of her brand-name anti-seizure drugs cost about $370 in the gap last year, and the other about $270. This year Friedman paid about $150 and $130 for a month’s supply.

Medicare covers about 47 million older and disabled people, and about nine in 10 have some kind of prescription plan. Most rely on the drug benefit, also known as Part D, which is delivered through private insurance plans.

Beneficiaries have until Dec. 7 to change their drug plans for 2012. Consumer advocates recommend that seniors check their coverage during open enrollment to see whether their current choice remains the best for next year.

The coverage gap starts after a beneficiary and his or her drug plan have spent a total of $2,840 on medications for the year. Seniors are then on their own for the next $3,600.

Once total spending reaches about $6,440, Medicare’s catastrophic coverage kicks in and beneficiaries pay only a token amount. Most people do not spend enough in the doughnut hole to qualify for catastrophic coverage.

The Republican-led Congress that passed the drug benefit under President George W. Bush was trying to balance coverage and costs, as many conservatives fretted about creating a new unfunded entitlement. Under Obama’s health-care law, the gap will be gradually phased down by 2020.