A new study about physical activity, obesity, and mortality has been propagating so many headlines and so much commentary, it’s pretty much a given that if you are seeing this, you have seen something like: “Inactivity kills more than obesity.”

As is generally true in such cases, few of the people opining about the study seem to have actually read it. I suppose that’s understandable — once you get to particulars about “random-effects meta-analysis,” the typical reader’s eyes glaze over. Still, it does prove helpful to read a study before interpreting it, however inconvenient our culture may find such labor.

Having braved that burden, here is what the study actually showed.

First, going from inactive to moderately active was, indeed, associated with marked reductions in premature mortality risk across all levels of body-mass index. That sounds at first like a validation of the idea that being fit trumps being fat. But there’s more. In the data tables, almost all of the moderately active to active people had BMIs below 30. The numbers of those both obese but also moderately active to active were very, very low. This recapitulates a finding published before: It is possible to be fit but fat, but few people actually are. Generally, being active is associated with weight control.

Second, the investigators looked not only at BMI, but also waist circumference — a far better measure not just of body fat excess, but its distribution. Not all overweight and obesity is a threat to health, but excess fat around the middle is. We have long known that not all variations on the theme of more weight correspond to more mortality.

Just as they compared varying levels of activity across levels of BMI, the authors compared varying measures of waist circumference across levels of exercise. The result was that going from a high to normal waist circumference was associated with almost the identical reduction in mortality risk as going from inactive to moderately active.

So, really, fitness and fatness both matter. Excess weight from muscle, with a lean waist, is not a risk factor for premature death. Excess body fat distributed in the lower extremities, as often prevails in premenopausal women, is also not a marker of risk. Weight around the middle is, however, and its effect on mortality appears in this large analysis to be much the same as the risk of inactivity.

Frankly, I think this is a better and more empowering message. If you have excess weight around your middle, and can reduce that whether with more exercise or by eating better, you will likely reduce your risk of mortality (and morbidity) meaningfully. If you are inactive and become moderately active, you will do the same — whatever your weight.

I’m not sure why we seemed so eager to paint this study as distilling two ways of improving health into one. Two is better. Besides, as noted, they tend to correlate highly anyway. Exercise more, you are apt to wind up weighing less — with potential benefit from both.

The hype in the headlines is the customary fiddling around. The reality in the data is that fitness and fatness both matter. Fortunately, we can do something about both.

David L. Katz is founding director, Yale-Griffin Prevention Research Center. He is the author of Disease-Proof: The Remarkable Truth About What Makes Us Well.