Last summer, Meghan Trainor’s doo-woppy single “All About That Bass” was seen by a lot of people as a body-positive empowerment anthem, with its condemnation of magazine Photoshop, and accompanying video of people of all sizes dancing in front of pastel backgrounds. But other people took issue with some of the lyrics—“I’ve got that boom boom that all the boys chase,” or “boys like a little more booty to hold at night.” Writers at Jezebel, Slate, and other publications accused the song of implying that self-esteem comes from male acceptance, that of course women shouldn’t worry about their size, because men still like them.

“Loving yourself because dudes like what you’ve got going on is a pretty flimsy form of self-acceptance,” Chloe Angyal wrote at Feministing. “In fact, it’s not really self-acceptance at all if it depends on other people thinking you’re hot.”

Trainor’s message might not be a perfect one, but new research shows it is effective. A recent study published in Social Psychological and Personality Science found that telling women men were attracted to non-stick-thin models increased their body satisfaction.

The researchers, from Southern Methodist University and Florida State University, had undergraduate heterosexual women look at images of plus-sized models (“plus-sized” in model terms—the models in the photos were estimated to be between a size 8 and 10, or “representative of the average female undergraduate,” the study says). In some cases, the width of the pictures was reduced by 30 percent, “to depict the thin-ideal.”

The women were either told that men picked the images because they found them attractive, or just that the images were taken from the media. In one experiment, another control group was told that men prefer thin women.

The participants reported higher satisfaction with their weight when they were told men were attracted to the average-sized models. But body satisfaction when women were told nothing was the same as when they were told men are attracted to ultra-thin women. This didn’t surprise the researchers, though.

“We did not expect women who were led to believe that men desired the ultra-thin women would necessarily feel worse about their bodies than the women who were not given any information,” they write. “The media already makes it clear that men desire ultra-thin women and we believed women told nothing would rely on this perception.”

With that sad conclusion in hand, the researchers tried one more test—telling the participants that other women preferred the average-sized models. That did nothing. The researchers suggest that “what women think men desire” may account for, at least partially, the relationship between the prevalence of super-thin images of women in the media, and poor body satisfaction among women who see those images. “For example, men in the media are more likely to date, provide physical affection to, and/or engage in sexual relations with thinner women compared to larger women,” the study reads. These portrayals may be part of why women tend to overestimate how thin men want them to be.

Perhaps it’s true that the purest form of self-esteem comes from the self and the self alone, or alternately, from a crystal-clear self-esteem spring in the mountains, probably with a lot of deer nearby. But most people’s springs are muddied in some way, by others’ expectations or what they perceive others’ expectations to be. And previous research has linked feeling accepted to women feeling “less concerned about their size over time…[suggesting] those women might have been driven to diet and exercise in healthier, more sustainable ways,” as my colleague Olga Khazan wrote. Feeling desirable could be one facet of that.