Assuming the COVID-19 vaccine would be in high demand, states put restrictions on who would get it first, hoping to make sure that it would reach the most vulnerable people before anyone else.

But since the first shot was administered last month, bigger problems than equity have emerged. A series of errors and challenges has left the U.S. with a decentralized vaccination effort whose major hurdle is getting the vaccine into the arm of someone — anyone — who needs it.

As states begin to ramp up vaccinations, they along with the federal government should take steps to remove the barriers that have caused such a slow start.

The Trump administration took the first such step this week as it suggested that states speed up the vaccination of high-risk frontline workers and people 65 and older by no longer holding back the second dose of the two-dose vaccine, a plan similar to what President-elect Joe Biden had announced days before.

That will free up more overall doses for use. In some states, the problem is not the supply of the vaccine itself but getting the right people in line to get shots. For those areas, the policy change will give those administering the vaccine more people to choose from.

When it was thought that the vaccine would be in limited supply, it made sense to hold back the second dose to make sure that the first people vaccinated received full protection. But the first phase of vaccination, for nursing home residents and health care workers, has gone slower than expected, in no small part because many of them, particularly in nursing homes, are refusing the vaccine.

But vaccine refusal isn’t a problem, not yet anyway. Instead of worrying about the workers who won’t take the vaccine now, those states should redirect those doses to people who want them, starting first with seniors and vulnerable public-facing workers.

Strict requirements aren’t the only issue. In some areas, including Maine, the problem appears to be more about the insufficient supply of vaccine being received. It will be left to the Biden administration to figure out how to break that bottleneck.

Once the supply side is figured out and a wider portion of the population becomes eligible for vaccination, there too has to be more places to get them. Some states are already using stadiums for mass vaccination events; Dr. Nirav Shah of the Maine Center for Disease Control and Prevention said the state is working on its plans.

Through the vaccination process, health officials should remain vigilant about equity. They should release detailed information on who is getting the vaccine and why — an area in which Maine has fallen behind other states — so that the public can evaluate its fairness.

After all, the people on the top of the list are there because, as a whole, vaccinating them first will save the most lives. They should get every chance to get the vaccine in a timely manner.

But some of them will refuse. And just as they have over the last month, logistical challenges are bound to disrupt delivery of the vaccine in one way or another, making it impossible to follow strict guidelines to the letter.

When that happens, vaccination programs need to be flexible enough to allow those doses to go to someone else. Even if it isn’t perfect, every shot is progress.