For fully vaccinated people, the risk of still getting COVID-19 -- described as "breakthrough infections" -- remains extremely low, a new study out of New York suggests.

Among 417 employees at Rockefeller University who were fully vaccinated with either the Pfizer or Moderna shots, two of them or about .5%, had breakthrough infections later, according to the study published on Wednesday in the New England Journal of Medicine.

"We have characterized bona fide examples of vaccine breakthrough manifesting as clinical symptoms," the researchers wrote in their study. "These observations in no way undermine the importance of the urgent efforts being taken at the federal and state levels to vaccinate the U.S. population. They also lend support to efforts to advance a new vaccine booster (as well as a pan-coronavirus vaccine) to provide increased protection against variants."

The researchers, from Rockefeller University, found that coronavirus variants with several differences from the original virus caused the breakthrough infections.

A variant that infected one of the patients had the mutation E484K, which was first found in the B.1.351 variant originally identified in South Africa. E484K has been called an "escape mutant" because it has shown it might be able to escape some of the antibodies produced by coronavirus vaccines. One of the mutations found in both study participants' infections included D614G, which emerged early in the pandemic.

One of the breakthrough infections was in a healthy 51-year-old woman who received her second dose of the Moderna vaccine on February 19. Nineteen days later, she tested positive for COVID-19 on March 10 after developing symptoms.

The other breakthrough infection was in a healthy 65-year-old woman who received her second dose of the Pfizer vaccine on February 9. She later learned that her partner, who was unvaccinated, tested positive for COVID-19 on March 3. In the following days, the woman developed symptoms of her own. She tested positive for COVID-19 on March 17.

More research is needed to determine whether similar findings related to breakthrough infections or variants would emerge among a larger group of participants from various parts of the United States.

Experts say that some breakthrough cases of COVID-19 in people who have been fully vaccinated are expected, since no vaccine is 100% effective.

Last week, the U.S. Centers for Disease Control and Prevention told CNN that the agency has so far received less than 6,000 reports of breakthrough coronavirus infections among more than 84 million people fully vaccinated nationwide.

The CDC said breakthrough cases occurred in people of all ages who had been vaccinated, but a little more than 40% were in people 60 or older. They were also more prevalent in females and 29% were asymptomatic.

The agency said it has developed a national database of COVID-19 breakthroughs so that state health departments can report them

"Vaccine breakthrough infections make up a small percentage of people who are fully vaccinated. CDC recommends that all eligible people get a COVID-19 vaccine as soon as one is available to them," the CDC said in a statement to CNN.