You might think that super-masculine features—strong jaw, bulging biceps, hairy chest—are the kinds of physical traits women typically find most attractive in men. After all, such manly features suggest that a guy has lots of testosterone and so could outcompete lesser males in life (and in love).

But according to a new study, what really turns women on is low (but not too low) body fat! Surprised? Here’s the scoop…

The same testosterone that makes a man look muy macho also has a downside—it can suppress the immune system. A theory called the immunocompetence handicap hypothesis holds that manly-looking men must be extra-strong and fit because they have overcome this handicap, and thus they would be primed to pass on good genes to their kids—which would naturally make them attractive to women. However, the new study pokes holes in this theory.

Researchers measured the body fat of 69 male volunteers ages 19 to 31. About 65% of the men were at a healthy weight…about 30% were overweight or obese…and about 5% were underweight. The men were photographed wearing just underwear. They also had blood tests to measure their levels of circulating testosterone. And—as a gauge of the strength of their immune system responses—they were vaccinated against hepatitis B and then had their antibody levels measured one month later.

Next, researchers asked 29 young women who were in the fertile phase of their menstrual cycles—a time when their hormones would make them most receptive to sexual cues and most responsive to masculine appeal—to view the photos and rate the men’s bodies and faces for sexual attractiveness. A different group of raters (women and men) assigned scores to each man’s photo based on perceived levels of masculinity. And a third group of women rated the men’s facial fatness, which is related to body fatness. Then the researchers compared the various ratings to how well the men’s immune systems had responded to the hepatitis B vaccine.

Results: Contrary to what the immunocompetence theory would predict, the men who had high masculinity ratings were not rated as the most sexually appealing, nor were their immune responses the strongest. Rather, the physical trait that ranked as most attractive among the women was having just the right amount of body fat—specifically, a relatively low 12% body fat (which would be typical of a man who was fit and slim, but not an elite athlete). Interestingly, the men with that physical trait also had the most robust immune system responses to the vaccine.

Guys, heed this: To attract women, or to be attractive to your woman, worry less about building massive muscles or cultivating the perfect beard stubble, and focus instead on achieving a slim-but-not-skinny physique through a healthful diet and regular exercise. To see how your current body-fat stats stack up to that 12% ideal, click here.

Editor’s note: Check out the study photos below. On the left is a composite image of the eight study participants with the lowest antibody response…on the right is a composite image of the eight participants with the highest antibody response. Which guy would you think would be more attractive to women? My vote goes to the one on the right—Mr. Healthy Immune System.