When it comes to HDL cholesterol, the standard message is that higher is better. Short for high-density lipoprotein cholesterol, this so-called “good” cholesterol is thought to help clear cholesterol from arteries, and exercise boosts levels of HDL cholesterol. People with low HDL levels have been shown to have a higher risk for heart disease, while people with higher HDL levels show the opposite.

But a large new study published in the Clinical Journal of the American Society of Nephrology found something unexpected: Higher HDL levels didn’t appear to be better at all. Using about a decade of data from 1.7 million male U.S. veterans, researchers found that while too-low levels of HDL cholesterol were associated with an increased risk of death from any cause, so were high levels of HDL cholesterol. Intermediate levels were associated with a lower risk of premature death.

“It was a U-shaped relationship, and that was a new and unexpected finding,” says Dr. Ziyad Al-Aly , assistant professor of medicine at the Washington University School of Medicine and co-director of the VA Saint Louis Health Care System’s Clinical Epidemiology Center. The strength of the study is its large participant base followed for a long period of time, but the observational study is heavily skewed toward older white men, and more research is needed with a more diverse population.

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The new data come at a time when clinical trials have repeatedly tested drugs designed to raise HDL cholesterol, only to have them fail to make improvements in heart disease. “The prevailing scientific thought was that if you increase something that was good, you might ameliorate outcomes,” Al-Aly says. But even when these medications did raise HDL cholesterol, the outcomes didn’t improve. “I think our analytic approach explains some of that,” he says. “Maybe too much of a good thing is actually a bad thing.”

Write to Mandy Oaklander at mandy.oaklander@time.com.