There’s been a lot of back-and-forth about fats in recent years. One change that’s gotten a lot of attention has been the idea that not only is fat not as bad as we once thought, but saturated fat really isn’t so bad either.

Last year, Time Magazine put a striking curl of butter on its cover to celebrate the rehabilitation of this spurned food item. But, as a new study shows, this kind of thinking may be a little premature, and we still don’t want to go crazy with saturated fat, since even if it has some benefits, it also has its downside.

Replacing saturated fats with refined carbohydrates had no beneficial effect on heart disease risk — but replacing them with healthy fats like unsaturated fats did have an effect.

“Our research does not exonerate saturated fat,” said Frank Hu, the lead author of the new study. “In terms of heart disease risk, saturated fat and refined carbohydrates appear to be similarly unhealthful. ”

Researchers examined data from over 120,000 people taking part in two long-term studies, the Nurses' Health Study and the Health Professionals Follow-up Study. All participants were healthy at the time the study began, and were asked questions periodically about their dietary habits, lifestyle factors like exercise and smoking, and any health problems they developed over the years. By the end of the study periods, which lasted from 24 to 30 years, more than 7,600 cases of coronary heart disease were recorded.

The Harvard School of Public Health team found that replacing saturated fats with refined carbohydrates had no beneficial effect on heart disease risk — but replacing them with healthy fats like unsaturated fats did have an effect. When they crunched the numbers, they were able to estimate that replacing 5% of one’s caloric intake from saturated fats with polyunsaturated or monounsaturated fats reduced heart risk by 25% and 15%, respectively.

Replacing saturated fats with complex carbohydrates, like those from whole grains, lowered the risk by 9%. But replacing them with refined carbs and sugars wasn’t linked to any reduction in heart risk at all.

“Our findings suggest that the low-fat, high-carb trends of the 1980s and 1990s are not effective in reducing risk of CHD,” author Yanping Li said in a statement. “It means that individuals should not replace saturated fat with refined carbs or vice versa. Dietary recommendations to reduce saturated fats should specify their replacement with unsaturated fats or with healthy carbohydrates, such as whole grains.”

The authors recommend making simple substitutions, like using canola oil, olive oil, or other vegetable oils rather than butter, lard, or hard margarine. Think about having peanuts, almonds, or olives as a snack instead of chips; and try avocados or lean chicken breast instead of processed meats or heavy cheeses.

It may take some time for the FDA to catch up, but their new recommendations are projected to relax their previously tight restrictions on fats. While the experts are still sorting it out, the best advice may be simply to eat a balanced diet, with as many real, whole foods as possible.

The study is published in the Journal of the American College of Cardiology.