Eggs likely aren’t responsible for high cholesterol—but new research may have found the real culprit behind rising cholesterol levels.

The study, published in The American Journal of Clinical Nutrition, found that the saturated fat in food, not dietary cholesterol in eggs, was linked to higher cholesterol levels. In fact, participants who ate two eggs a day for five weeks actually saw improved cholesterol levels. “When it comes to a cooked breakfast, it’s not the eggs you need to worry about—it’s the extra serve of bacon or the side of sausage that’s more likely to impact your heart health,” Jon Buckley, PhD, senior study author and executive dean of the University of South Australia Allied Health and Human Performance Academic Unit, said in a press release.

For years, researchers have gone back and forth on whether eggs raise low-density lipoprotein (LDL) cholesterol—the “bad” kind that can increase the risk of heart disease and stroke. This is because eggs are packed with cholesterol. One large egg contains around 200 milligrams (mg) of dietary cholesterol, two-thirds of the previously recommended daily limit of 300 mg. But more recent research has found that it’s actually the saturated fat in foods that raises LDL cholesterol. Most high-cholesterol foods are also high in saturated fat, Buckley told Health, but eggs have very little (1.6 grams), which sparked the debate.

“For much of the past two decades, we’ve had a pretty strong feeling that it’s saturated fat, far more than cholesterol [that raises LDL levels],” Sean Heffron, MD, preventive cardiologist at the Center for the Prevention of Cardiovascular Disease at NYU Langone Heart, told Health. The new study put this theory to the test.

Results showed that saturated fat was linked to a rise in LDL cholesterol, but dietary cholesterol was not. Also, compared to the control diet, the egg diet lowered LDL cholesterol (by an average of 5.7 mg/dL), but the egg-free diet did not. This suggests that saturated fat elevates LDL levels—not dietary cholesterol, Buckley said. “We were a bit surprised that the effect was so clear-cut,” he added.

It’s worth noting that the Egg Nutrition Center, a division of the American Egg Board, provided funding for the study.