Thousands of American service members are refusing to be vaccinated for the Covid-19 coronavirus, reports the Associated Press.

Some Army units are seeing as few as one-third agree to the vaccine,” the AP says.

“Military leaders searching for answers believe they have identified one potential convincer: an imminent deployment,” particularly in the Navy. Sailor heading to see last week, the news agency says, “were choosing to take the shot at rates exceeding 80% to 90%.”

Overall, the numbers are not so good.

In answer to a question at a Wednesday Congressional hearing, Air Force Maj. Gen. Jeff Taliaferro, vice director of operations for the Joint Staff,  said that “very early data” suggests that up to two-thirds of the service members offered the vaccine have accepted, the AP says.

The news agency notes that two-thirds is still higher than the roughly 50% vaccine acceptance rate among the general U.S. population, according to a recent survey.

So far, vaccinations are optional for service members, but that’s likely to change once the Pentagon gets approval from the Centers for Disease Control (CDC).

“We cannot make it mandatory yet,” Vice Adm. Andrew Lewis, commander of the Navy’s 2nd Fleet, said last week. “I can tell you we’re probably going to make it mandatory as soon as we can, just like we do with the flu vaccine.”

Officials from individual military services told the AP that for now, “refusal rates vary widely, depending on a service member’s age, unit, location, deployment status and other intangibles.”

At Wednesday’s House hearing, Rep. Mike Rogers (R-AL), asked Gen. Taliaferro if unvaccinated troops are deployable.

Taliaferro said they are, adding that a command structure set up in the past year allows all branches of the military to “operate in a Covid environment,” The Hill reports.