Saturated fat has been a controversial subject in recent years, with some research suggesting that it may not be as bad for health as once thought. But a new study published in The BMJ dashes any hope that butter is actually back.

Cutting down on saturated fatty acids—found in animal foods, like dairy and meat, as well as palm and coconut oil—may lower risk of coronary heart disease, according to researchers. And swapping these foods for unsaturated fats (from vegetable oils, nuts, seeds, avocados, and seafood, for example), whole grains, and plant-based proteins (think lentils and edamame) seems to boost heart health even further.

The new findings are significant because saturated fat has been a source of debate: Studies have shown that saturated fatty acids can affect cholesterol, but there's hasn't been any definitive research linking them to overall heart health. A large meta-analysis published this summer, for example, found that butter consumption does not appear to raise heart disease risk.

The current U.S. Dietary Guidelines have taken a conservative approach to saturated fats, saying they should make up no more than 10% of total calories. Qi Sun, MD, assistant professor of nutrition in the Harvard T. H. Chan School of Public Health and senior author of the new study, says his group’s findings back up this advice.

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The new study also bolsters government recommendations for “eating an overall healthful diet," Dr. Sun told Health—one that includes fruits, vegetables, whole grains, vegetable cooking oils rich in polyunsaturated fats and monounsaturated fats (the two main types of unsaturated fats), nuts, legumes, fish, and low-fat dairy.

To determine saturated fat’s long-term effects on heart health, he and his colleagues followed more than 73,000 women and 42,000 men for an average of 26 years, collecting data on their diet and health every four years.

After controlling for factors such as age, ethnicity, and other potential influencers, the researchers found that participants who consumed the most calories from four commonly consumed saturated fatty acids—lauric acid, myristic acid, plametic acid, and stearic acid—were 18% more likely to develop coronary heart disease over the course of the study than those who consumed the least.

Some researchers have suggested putting individual limits on each of these fatty acids, said co-author Frank Hu, PhD, professor of nutrition and epidemiology, in a press release. But that’s not practical, he argues, since they share many of the same food sources: red meat, dairy fat, butter, lard, and palm oil.

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Instead, it is healthier to focus on lowering total saturated fat intake, says Hu. In fact, the researchers estimated that replacing just 1% of those fats with the same number of calories from poly- or monounsaturated fats (think avocado and nuts), whole grains, or plant-based proteins could reduce heart disease risk by 4% to 8%.

The study specifically recommends swapping animal fats (butter and lard) with vegetable oils high in unsaturated fat; and points out that restaurant food, and snacks and bakery items—including crackers, chips, popcorn, cakes, and cookies—can be high in saturated fat.

The researchers also offer some insight as to why prior studies haven't always shown a clear link between less saturated fat intake and better heart health. Often, the authors say, people who cut back on saturated fat replace those calories with low-quality carbs, like processed food and refined flour. These are associated with health risks of their own, and likely cancel out any health benefits.

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This is the largest observational study to-date to examine the association between specific saturated fatty acids and the risk of coronary heart disease, say the authors, and its results are in line with previous research that has focused specifically on healthy swaps.

While the findings aren’t terribly surprising, they do serve one important purpose: As Hu put it, “this study dispels the notion that ‘butter is back.'"