Millions of Medicare Advantage customers are fast approaching a deadline for a task they'd rather avoid: Researching and then settling on coverage plans for 2015.

The annual enrollment window for the privately run versions of the government's Medicare program for the elderly and disabled people closes on Sunday. This is the main opportunity most customers have each year to adjust their health coverage, and it may be worth paying extra attention to the details.

Insurers frequently tweak their coverage plans from year to year, but brokers and other industry insiders say they're seeing more changes over the last few years as companies weed out lower-quality coverage and adjust to government funding cuts.

About 4 percent of Medicare Advantage enrollees, or roughly 480,000 people, will have to find new coverage for 2015 because their current plan won't exist, according the nonprofit Kaiser Family Foundation, which studies health-care issues. Last year, more than 500,000 people faced that choice.

Customers who lose their old plans may be eligible to pick coverage in a special election period that runs through the end of February.

Other customers with discontinued plans are being automatically enrolled in another option offered by the same insurer. Companies generally try to limit the coverage changes in these cases, but the plans may not be identical, especially when comparing premiums.

"It really pays to shop around," said Dwane McFerrin, a vice president with Senior Market Sales Inc., which helps agents sell Medicare Advantage coverage.

However, sitting down to figure out coverage changes or whether there's a better option can trigger headaches. Customers need to make sure their new plan covers all their doctors and prescriptions and leaves them with manageable bills if a major health problem hits.

Plus, they have to make sure the price or premium is right.

Almost 16 million people are covered by Medicare Advantage plans, nearly twice the total covered just seven years ago, according to Kaiser. The foundation's researchers have found that people have, on average, 18 plans to choose from, but they generally prefer to stick with what they have and find it daunting to review all those options.

Insurers say those choices are changing more than in the past because years of funding cuts have forced them to trim the number of plans they offer or adjust their benefits.