Today’s high-earning women are justly proud of their paychecks—I explore the rise of the female breadwinner in this week’s TIME cover story—but they still often feel that men will be intimidated rather than attracted to them as potential mates.They think that their success will seem too threatening, and be held against them. As a result, some women in the dating pool devise camouflage mechanisms.A young ob-gyn working in Pittsburgh tells men she meets that she “works at the hospital, taking care of patients”—subtly encouraging the idea that she’s a nurse, not a doctor.When a university vice-president in south Texas was on the dating market, she would vaguely tell men she worked in the school’s administrative offices and avoid letting them walk her to her car for fear they would see her BMW. “I want them to give me a chance,” says the Pittsburgh doctor. “I want them to at least not walk away immediately.”But a growing body of research shows that, while there may have once been a stigma to making money, high-earning women actually have an advantage in the dating and marriage market.In February 2012, the Hamilton Project, a Brookings Institution initiative that tracks trends in earnings and life prospects, found marriage rates have risen for top female earners—the share of women in the very top earning percentile who are married grew by more than 10 percentage points—even as they have declined for women in lower earning brackets. (The report also suggested that the decline in those lower brackets may be because women can support themselves and are dissuaded from marriage by the declining earnings of men.)We got the first indication of a major shift back in 2001 with a study by University of Texas at Austin psychologist David Buss that showed that when ranking traits that were important in a marital partner, there had been a striking rise in the importance men gave to women’s earnings and a sharp drop in the value they place on domestic skills. Similarly, University of Wisconsin demographer Christine Schwartz noted in a 2010 study in the American Journal of Sociology that “men are increasingly looking for partners who will ‘pull their own weight’ economically in marriage,” and are willing to compete for them.Indeed, men may be ready to cede their role as breadwinner than they are given credit for. Last year, Stanford University economist Ran Abramitzky, working with two European colleagues, published a fascinating study that suggests exactly this.Looking at demographic records for the French population after World War I, they found that men in regions that had suffered higher mortality rates (and were therefore short on men) were more able to “marry up.” Given the opportunity to marry into a life with more resources and prospects, the men hastened to do so. To Abramitzky, the surprise was “how flexible this marriage market was” and how quickly men were able to adapt to the changing demographics.Now that women are poised to become the major breadwinners in a majority of families within the next generation, this research suggests that men will be just as adaptive and realize what an advantage a high-earning partner can be. Men are just as willing as women to marry up, and life is now giving them the opportunity to do so. So women, own up to your accomplishments, buy him a drink, and tell him what you really do.