Vaccines against COVID-19, while protective against hospitalization and death, may not be great at preventing long COVID after breakthrough infections, a new study finds.

Epidemiologists associated with the US Department of Veteran Affairs looked at the medical records of 13 million individuals—mostly white male veterans aged 60 on average—including almost 34,000 who experienced breakthrough COVID-19 infections after vaccination. They found that while being vaccinated greatly reduces risk of hospitalization and death, vaccines only reduce the risk of long COVID by about 15 percent, as the researchers reported in a paper published on Wednesday in Nature Medicine.

Vaccinated individuals experiencing breakthrough infections were protected from certain symptoms, like blood clots and lung disorders. But there was no difference between the vaccinated and unvaccinated when it came to longer-term risks of infection, which include neurological issues, gastrointestinal symptoms, kidney failure, and other conditions.

“This was disappointing,” Ziyad Al-Aly, lead author and chief of research and development service at VA Saint Louis Health Care System, told The Washington Post. “I was hoping to see that vaccines offer more protection, especially given that vaccines are our only line of defense nowadays.”