Though it had long been assumed that fitness was more important to health than a bit of excess fat, research is now beginning to show that weight may be even more important than fitness. A study last last year found that being overweight itself is a risk factor for heart disease and heart attack. This week, a new study published in European Heart Journal has shown that weight could even be more of a risk factor than fitness levels.

The new study looked at over 740,000 Swedish men who entered their compulsory national service from 1969 to 1984. Study subjects’ fitness levels were measured at the time, as were their height and weight. The men in the study were followed until January 2011.

Researchers found that those men most physically fit at age 18 had a reduced risk of heart attack later on in their lives. However, the study also found that those men who were physically fit but overweight or obese at 18 had a “significantly” higher risk of heart attack later in life than those men who were not physically fit but were “lean.”

“While being physically fit at the end of your teens can reduce the risk of heart attack, fitness alone does not appear to fully compensate for the risks with being overweight or obese,” said Peter Nordström, co-author of the study and a geriatrics professor at Umeå University. “In other words, having a normal weight is more important than being in good physical shape, but it is even better to be both fit and have a normal weight.”

The study found that “regular fitness training” is associated with a 35% decrease in risk for a premature heart attack. The study’s authors did caution, however, that the study was unable to determine that high fitness levels are specifically what reduces the risk for heart attacks.