A majority of people with private health coverage purchased through Covered California are keeping their plans for a second year, according to new figures that the state-run insurance exchange released on Wednesday.

During Covered California’s first year, 1.2 million people bought private coverage and more than 1.1 million people kept it. Of those, about 1 million are eligible to renew. As of last month, 576,000 of them had allowed their plans to renew automatically, Covered California says.

Another 368,000 had decided to shop around, though as of December only 54,000 had switched plans, it adds.

Covered California Executive Director Peter Lee says the small number of people who had switched  is an indication that most Californians are satisfied with the coverage they’re getting.

"Consumers liked the plan they were in, liked the providers they have access to, and did not see the need -- even though one-third actively logged onto the system and looked around -- to change coverage," he says.

Not everyone who bought private coverage last year needed to, or could, renew. Some gained job-based coverage, and about 85,000 became eligible for Medi-Cal because of changes in their income, Lee notes.

Californians have until Feb. 15 to enroll in or change their health coverage.