Success has its price. In the case of women who rise to the upper echelons of corporate America, that sacrifice may mean feeling less physical and mentally healthy than their lower-earning and less educated counterparts, according to a new study published in the Harvard Business Review.

That’s a big surprise. For years studies have shown a strong correlation between higher incomes and good health. As the National Bureau of Economic Research puts it, “Richer, better-educated people live longer than poorer, less-educated people.” The Centers for Disease Control and Prevention has also noted that higher education and income levels are key to improved health.

Study author Meghan FitzGerald—who is EVP of strategy, M&A and health policy at Cardinal Health and a member of the World Economic Forum’s Global Agenda Council on Aging—knows that research well. But, she writes in HBR, she still couldn’t help by wonder whether the “long hours, travel, and lack of consistent sleep” required by many executive positions “would take an insidious toll.”

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FitzGerald surveyed 369 women 21 to 60 years old, many of whom work for Fortune 500 companies, asking a series of questions about health-related personal habits, incomes, education levels, age, marital status, ethnicity, weight, and height.

The results were mixed. On one hand, the higher a woman’s income or education level, the less likely she was to be overweight or drink to excess, and the more likely she was to get at least six hours of sleep a night.

And yet, when asked about their sense of physical and mental health, that correlation changes. FitzGerald found that the more educated and wealthy the women, the more likely they were to say that they felt less healthy on a scale of 1 to 5, where 5 was most healthy and 1 the least healthy. For example, women making between $20,000 and $50,000 a year reported an average health score of 2.5. But for women who made more than $1 million a year, the typical score dropped to less than 2. Similarly, women with a high school diploma reported an average score over 2.5, while those with a doctorate reported about 2.

According to additional data FitzGerald provided to Fortune that did not explicitly appear in the paper, education was a strong predictor of how many days in the previous month women felt that their physical or mental health was not good. High school graduates reported less than 2 days of bad physical health and just over 2 days of bad mental health. For those with doctorates, the numbers were about 3 and more than 6, respectively.

As the published paper indicated, more educated women were twice as likely as those with less education to say they had an alcoholic drink within the previous month, but women with less education would consume an average of 2.5 to 3 drinks at a sitting, versus 1.5 for those with more education.

When matched to income alone, those with higher incomes were more likely to have had a drink in the previous month, but there was no significant difference in the amount consumed at one time. Women earning $1 million or more a year were, however, four times more likely to worry about drinking too much than those earning between $20,000 and $50,000.

From the study data, it’s impossible to say whether the wealthier and more educated women were actually in better health than those with less money and education. FitzGerald assumed that given their places of employment, most of these women likely had access to health care. However, 30% of those in this cohort reported a weight gain because of stress and 48% said they had not been able to see a doctor because of their workload. At all income levels, most agreed that attractiveness was an important factor in income success.

“I believe [higher income and more educated] women do have stress and more migraines and psycho-social issues,” FitzGerald told Fortune. However, the negative health impacts associated with being a high-powered female exec has remained largely unknown, says FitzGerald, because “women are masters of discretion” and assume that they cannot broadly talk about some types of issues.

“Ten years ago no one would have talked about this,” she said. “‘Suck it up, shut up, go have your migraine in the bathroom.’ I don’t think they’re calling in sick because quite frankly they can’t. They’re all working second shifts [caring for their families after they come home from work each day].” The result could be a factor in the under-representation of women in upper management, FitzGerald thinks. As women climb the corporate ladder, increasing pressures at both work and home might convince many women to abandon their original career objectives, reducing the pool of talent that could move into executive positions.

“Is anyone opting out of that upper echelon pool saying it’s not worth the journey?” FitzGerald said. “Is there something about that group that makes it difficult from a health perspective or psycho-social perspective [to reach top management]?”

One point the study does not address is how the women’s responses compare to their male counterparts. FitzGerald says she’s currently working on a second study to give a wider view of the issue.