Ben & Jerry might help you get pregnant, but not in the usual way. A diet rich in ice cream and other high-fat dairy foods may lower the risk of one type of infertility, a study suggests.

It sounds too good to be true and probably is, some doctors say.

But the findings are bound to get attention because they are from the well-known Nurses Health Study at the Harvard School of Public Health and were published Wednesday in the European journal Human Reproduction.

Researchers found that women who ate two or more low-fat dairy products a day were nearly twice as likely to have trouble conceiving because of lack of ovulation than women who ate less than one serving of such foods a week.

Conversely, women who ate at least one fatty dairy food a day were 27 percent less likely to have this problem.

Even the researchers say women should not make too much of these results, which are based on reports of what women said they ate over many years — not a rigorous, scientific experiment where specific dietary factors could be studied in isolation.

"The idea is not to go crazy and start to have ice cream three times a day," said the lead author, Dr. Jorge Chavarro, a research fellow at Harvard. "But it is certainly possible to have a healthy diet with low saturated fat intake by having one serving of high-fat dairy a day."

Others urged caution.

"A good healthy dose of skepticism is good for people," especially when the results are so hard to swallow, said Dr. Patrick Remington, a University of Wisconsin-Madison epidemiologist.

After all, the Nurses Health Study also found that menopause hormones could ward off heart disease — something doctors believed until a more scientific study disproved it several years ago, he noted.

The new research doesn't even apply to most cases of female infertility — not ovulating is to blame only one-third of the time.

The study also found no link between infertility and dairy foods in general — something that bothered another statistics expert, David Allison at the University of Alabama at Birmingham.

Instead, researchers only saw a link when they separated non-ovulating women who ate yogurt and other low-fat dairy products from those eating more high-fat varieties.

When they looked at specific foods — and this is where the numbers really get tricky — they found that women eating ice cream two or more times a week had a 38 percent lower risk of infertility than women consuming ice cream less than once a week.