More than two-thirds of Californians who were uninsured at the start of the Affordable Care Act’s implementation have since gained health-care coverage, according to a new report.

Prior to the coverage expansions created by the ACA—also known as Obamacare—California had the nation’s largest population of uninsured non-elderly adults at nearly six million.

Most of those people wanted health coverage but felt they couldn’t afford it, according to the Kaiser Family Foundation, which has followed a group of Californians who were uninsured in the summer of 2013 as part of a longitudinal survey on the effects of the ACA, which has been roundly rejected by Republican-held state legislatures for the past two years.

By 2014, 58 percent of those previously uninsured had purchased coverage during the state’s first open enrollment period: 1.6 million had enrolled in Medi-Cal, the state’s version of Medicaid, and another 1.4 million had bought private insurance through Covered California. During the state’s second open enrollment, which ended this year, an additional 1.3 million people enrolled in coverage, bringing the total number of newly insured up to nearly 4.3 million.

That leaves some 1.7 million people still without insurance in the state.

“For the people that didn’t have health insurance, California has been very successful in enrolling two-thirds of that group,” Mollyann Brodie, senior vice president at the Kaiser Family Foundation, told the Los Angeles Times. “But the group that is left is a harder-to-reach group.”

That group is comprised in large part of undocumented immigrants who are barred by law from receiving coverage through the ACA. Deferred Action for Childhood Arrivals (DACA) recipients in California have been eligible for Medi-Cal since the beginning of 2014. And this year, Gov. Jerry Brown approved in his budget a measure that expands Medi-Cal eligibility to all children in the state, no matter their immigration status.

A bill, SB 4, which would expand Medi-Cal to include undocumented adults and allow those adults to purchase private insurance through Covered California, is currently being considered in the Democratic-led state assembly.