Advisers to the Food and Drug Administration voted unanimously on Friday to authorize a third dose of the Pfizer-BioNTech vaccine at least six months after the initial two doses to those 65 and older and others deemed high risk for severe covid-19. Though I wish the agency went further to allow boosters for all adults, I think the FDA reached a reasonable decision — one that I hope will be reaffirmed this week by the Centers for Disease Control and Prevention.

The evidence is growing that while the coronavirus vaccines provide excellent protection, immunity declines over time. Last month, the CDC director presented preliminary results that while the vaccines continued to safeguard well against severe disease, effectiveness against mild or asymptomatic infection waned from 92 percent to 64 percent. A CDC study found that protection for nursing home residents dropped from about 75 percent to 53 percent, and another study of Kaiser Permanente patients found a decrease from 88 percent to 47 percent.

Data from Israel provide another crucial data point: A third dose of the Pfizer vaccine provided additional immunity, with comparable side effects to the first two doses. According to a new study published in the New England Journal of Medicine, for Israelis 60 and older, the booster dose increased protection against symptomatic infection more than 11 times and against hospitalization by nearly 20 times.

There are some who argue that as long as data from the United States show that two doses protect well against severe disease, a third shouldn’t be given. There are two problems with this reasoning. First, there are many medically vulnerable individuals for whom a mild bout of covid-19 could land them in the hospital. If a booster could help avert a breakthrough infection, it could save them unnecessary suffering.

Second, Israel has already noted waning protection against severe disease. Its mass vaccination campaign preceded ours and its data collection is far superior (recall that the United States had, inexplicably, stopped tracking breakthrough infections back in May). We shouldn’t wait to heed Israel’s lessons.

Then there’s the World Health Organization urging that wealthy countries hold off on boosters until there is more equitable global vaccine distribution. Here, I agree with the Biden administration: This is a false choice. At least 15 million doses of the coronavirus vaccine have been discarded in the United States already, and millions more will soon expire. There is no mechanism to repurpose these unused doses for export. Instead of letting them go to waste, why not allow them to go to vulnerable Americans?

Some experts have also argued that boosters are not the answer to stemming the current coronavirus surge. They’re right; from a public health standpoint, it’s more important to get the first dose into the unvaccinated than a third dose to the vaccinated. Again, though, this shouldn’t be an either-or. Lack of supply is not the reason about 70 million Americans are refusing to be inoculated. Denying the vaccinated a booster isn’t going to persuade the unvaccinated to get the shot instead.

If it were up to me, I would have allowed all adults who want a booster to access it. That’s because people’s perception of risk is different, and individual risk decisions should be left to patients — in consultation with their doctors — rather than a federal health agency. One person could look at the existing data and determine that they will hold off until it’s clear that everyone needs a third dose. Another person could look at the same data and clamor for the booster now because they want to avoid even a mild case of covid-19. Just as vaccinated people are making different decisions about their risk tolerance for everyday activities, they should be able to choose whether they want the added protection of the third dose.

The FDA advisers came to a compromise by recommending authorization of the booster for those who are older or otherwise at higher risk for severe covid-19. It’s now up to the CDC to delineate what constitutes this risk. I hope that it will come to the broadest possible definition. People with any underlying medical condition should be able to obtain the booster, and without a doctor’s note. The CDC should not restrict occupational exposure to health-care workers; I believe it should give the option to everyone who is required to work in-person. It should also permit higher-risk personal situations, including living with unvaccinated family members.

When vaccines first became available, federal health officials made the eligibility criteria so strict that they became a bureaucratic nightmare and substantially hindered the rollout. They shouldn’t make this mistake again. The FDA has already determined that a third Pfizer shot is safe and effective for many Americans. The CDC should endorse its recommendation and allow boosters for anyone who perceives themselves at higher risk.