Nutritionists have spent the past few decades trying to steer Americans away from saturated fats such as butter, lard and even coconut oil, but their effort hasn’t been as successful as it might have been. The campaign to curb cardiovascular disease has actually had the opposite effect. American waistlines have expanded, and the nation is suffering from an epidemic of Type 2 diabetes. A new report prepared for the American Heart Association explains why. Fat-conscious eaters cutting back on saturated fats often replaced the unhealthy fat with refined carbohydrates and sugars.

Americans turn to high-calorie foods that were low in nutrition to satisfy their craving for needed calories, according to researchers led by Dr. Frank M. Sacks, professor of cardiovascular disease prevention at the Harvard T.H. Chan School of Public Health.

Dr. Sacks’ team looked at four “core” trials conducted in the 1960s. The studies studied participants who reduced their consumption of saturated fat and replaced it with vegetable oil rich in polyunsaturated fat. The substitute fat was primarily soybean oil free of trans fats.

The substitution lowered participants’ coronary heart disease by 29 percent. That result is similar to the benefit from taking a statin to reduce cholesterol.

A later study followed 252 British men who had suffered heart attacks. They followed a low-fat diet that was high in carbohydrates such as refined, low-fiber flours and sugars. These are carbs that encourage promote weight gain and diabetes, two leading risk factors for heart disease. Their high-carbohydrate diet made virtually no difference on future heart attacks. Their cholesterol levels were reduced by only 5 percent.

Studies in North America and Europe saw people lowering their consumption of saturated fat but turning to refined grains, fruit juice, sweet desserts and snacks, sugar-sweetened beverages. The most important influence on study participants’ health was the types of food they ate instead of saturated and other fats.

Here’s some blunt advice that Sacks gleaned from the research: Consume few saturated fats like butter, full-fat dairy, beef and pork fat, and coconut, palm and palm kernel oils. Replace them with natural vegetable oils high in polyunsaturates — corn, soybean, safflower, sunflower, peanut, walnut and grapeseed oils, he said. The researcher also advocated the health benefits of canola and olive oil, which are rich in both monounsaturates and polyunsaturates.

“The average American diet is not very healthy,” said Dr. Walter Willett, professor of epidemiology and nutrition at the Harvard T.H. Chan School of Public Health.  He said the National Health and Nutrition Examination Survey shows “almost half the calories in the American diet come from carbohydrates, and of those 80 percent are from refined starches, sugar and potatoes.” He described dairy fat as “not optimal — not nearly as good as plant fats but not quite as bad as other animal fats.”

“You don’t have to totally abandon cheese, but dairy foods should be limited to one serving every one to three days, not three servings a day,” said Willett.

Read More: Good Fats, Bad Fats