We’ve all seen it in the grocery stores. Low-fat and fat-free choices are everywhere. Saturated fats — think fatty beef, lard and butter — are often associated with increased risk of heart problems. But a new study has suggested this may not be true.

The study suggests moderate fat intake and eating more fruits and veggies and fewer carbohydrates may lower your health risks. Researchers from the Prospective Urban Rural Epidemiology, or PURE, study surveyed over 135,000 respondents from five continents. They then followed them for an average of seven years. Their findings suggest that higher consumption of the major dietary fats — including saturated, monounsaturated and polyunsaturated fats — is associated with lower mortality.

The American Heart Association recently released a report that advised against the use of coconut oil because of high levels of saturated fats. But the PURE study says saturated fats are actually associated with lower stroke risk. The study suggests moderate consumption of fats — around 35 percent of one’s daily calories — is associated with a longer life span.

One problem the researchers found is people often replaced fats with refined carbohydrates, and this higher level of carbohydrates was associated with higher mortality. Another is that while dietary guidelines call for a minimum of five daily servings of fruits and vegetables, these can be expensive and unaffordable for low-income people.

If you’re looking for a dietary goal, remember the lowest risk of death was among those who ate a modest amount of fat plus three to four servings of fruits and vegetables. As for the carbs? Kick them to the curb.