The headlines are coming fast and furious: United Airlines is firing nearly 600 workers who have refused to follow its vaccination mandate. This or that hospital chain is firing a couple hundred workers for the same reason. While those headlines do show that companies are serious about their vaccination mandates, they’re obscuring the most important point: The results show that mandates work, and the number of people quitting or getting fired is tiny compared to the number of people getting vaccinated.

Take United. The 593 workers being fired for refusing to be vaccinated, and even the 3% who have requested exemptions from the requirement, are a tiny minority of the company’s workforce of 67,000 people in the United States. The company is still getting plenty of applications for jobs it posts, too, with 20,000 applications for 2,000 flight attendant positions.

When Delta Airlines announced that unvaccinated workers would pay a $200 a month surcharge to be on the company health plan, 20,000 workers were unvaccinated. Within a month, nearly 9,000 got a shot—a major improvement, but not approaching United’s level of success. Strong encouragement works, in other words, but not as well as outright requirement.

In one poll, 16% of people said they would quit or look for another job if their employer required vaccination. But so far, the numbers of people following through on that claim are much, much smaller. At Indiana University Health, 125 people quit … out of 35,800 employees. At Novant Health, a North Carolina-based hospital chain, 175 people were fired for refusing vaccination … out of 35,000 employees. And the firings came after 375 workers were first suspended, and 200 of them chose vaccination. Similarly, of the dozens of Massachusetts state troopers who reportedly planned to quit over a vaccination mandate, only one has actually done so.

Mandates spur a whole lot of big talk, but not so much action.

New York’s mandate for health care workers went into effect on Monday. The results? As of Monday, “92 percent of the state’s more than 650,000 hospital and nursing home workers had received at least one vaccine dose, state officials said. That was a significant increase from a week ago, when 82 percent of the state’s nursing home workers and at least 84 percent of hospital workers had received at least one dose.”

In Kansas City, Truman Medical Centers/University Health required vaccination, and just 39 out of 5,000 workers left.

A worker at the Curry Up Now restaurant chain who had hesitated to be vaccinated but now has her first shot after her employer mandated either vaccination or twice-weekly testing told the Associated Press, “It’s a good thing we’re required to get the vaccine, to ensure people’s safety.”

Tyson Foods, one of the meatpacking companies that have been slammed with COVID-19 outbreaks, instituted a vaccine mandate, and within less than two months, with a month to go before the requirement kicks in, the first-shot rate among its workers had gone from 50% to 80%.

This is the way forward. While masking and other precautions are very important until vaccination rates rise and daily case rates drop dramatically, the U.S. needs more people vaccinated to lower the rates of serious illness and death and clear out ICUs. Even so, a tiny minority of people will refuse, but for many more people who were genuinely just hesitating and being told it’s vaccination or your job, these requirements will work. They’re working already.