There’s “no doubt” the U.S. has undercounted its number of deaths from Covid-19, which now stand at over 581,000, President Joe Biden’s top medical adviser said.

But Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, said on NBC’s “Meet the Press” that a University of Washington analysis published May 6 that the true toll is probably over 900,000 is “a bit more than I would have thought.”

“Sometimes the models are right on line, sometimes they’re a bit off,” he said.

With the U.S. vaccination pace slowing, Fauci said using “trusted messengers” will be an important way to overcome hesitancy in some communities and get the nation closer to an 80% vaccination rate.

“It could be sports figures, it could be entertainment figures, it could be clergy or it could be your family doctor,” he said.

He spoke hours after celebrities from Prince Harry to Jennifer Lopez appeared on a TV and streaming special about the importance of vaccines. Biden and the first lady also recorded remarks for the event, as did Pope Francis.

The wider use of walk-in clinics or pharmacies is another major strategy to “get that last group of people who seem to be recalcitrant,” Fauci said, by making the process easier.

Looking ahead, if the U.S. reaches Biden’s current goal of 70% or more people having at least one shot by July 4, “you may see blips, but if we handle them well, it is unlikely that you’ll see the kind of surge that we saw in the late fall and the early winter,” he said.