What he could not get in one act during his first administration, President Bill Clinton is taking a little bit at a time during this one. Millions of Americans, particularly seniors, could benefit if the White House’s slow push toward universal access to health care continues.

Two announcements this week — one large, one small, both important — highlight the administration’s approach to expanding health care services. The big issue was protecting Medicare recipients from access and service problems.

The drive to cover large numbers of people for the lowest price possible has pushed some health maintenance organizations toward healthier populations while they try to slow down the way less-well people use their health insurance. The new rules announced by the president this week demand, for instance, that an HMO cover treatment of any condition “that a prudent layperson” would consider an emergency. The rules smooth access to specialists for patients who are directed toward that level of care. They clarify that HMOs may not pick only the healthy to cover. The health plans may not discriminate against Medicare recipients by limiting or denying coverage on account of physical or mental illness, genetic information or prior medical history.

The smaller announcement concerned children’s health services. Maine, like the rest of the nation, offers important health services to children that either their parents do not know exist or do not know they qualify for them. Under the program also announced by the president this week, leaders of eight federal agencies will send notices urging qualified families to sign up for Medicaid services. The advantage to getting everyone who qualifies to use this program is clear: innoculations completed in time to start school; health problems caught earlier; small illnesses seen in a primary-care office rather than the emergency room.

Though business owners understandably cringe at the thought of more orders from the feds, the seemingly contradictory directions of the robust economy and increasing numbers of uninsured workers suggest that the free market isn’t the answer to missing health insurance. The fact that the cost of health care continues to rise beyond inflation helps explain some of this trend but it also means that fewer and fewer low-wage workers can afford their own insurance.

Congress, both sides of the aisle, generally has been receptive to this incremental approach to health care. Going slowly does not ensure that each piece of the system will be put together thoughtfully — Medicare’s home-health care reimbursements are proof of that. But it does force opponents to raise specific objections to access for the elderly or children or the poor, rather than simply trashing the general idea of universal access.

In a far-from-perfect system, that’s one way to get progress.