In her bestselling book “Lean In: Women, Work and the Will to Lead,” Facebook chief operating officer Sheryl Sandberg faulted women for not “leaning in,” that is, not being aggressive enough in pursuing their career goals.

“We hold ourselves back in ways both big and small, by lacking self-confidence, by not raising our hands, and by pulling back when we should be leaning in,” Sandberg wrote.

The fact that women get paid less and are offered fewer opportunities than men is hardly news. A 2003 Harvard Business Review article entitled “Nice Girls Don’t Ask” reported that male MBA graduates from Carnegie Mellon were paid 7.6 percent, or almost $4,000, more on average than their female counterparts in their first job out of school. While 57 percent of the men responded to the initial salary offer by asking for more, only 7 percent of the women tried to negotiate a better deal.

So the solution should be simple — just get women to raise their hands faster, to ask for more, right? Not so fast. As the HBR article explained, there are good reasons why women are reluctant to ask for their due: “Women who assertively pursue their own ambitions and promote their own interests may be labeled as bitchy or pushy. They frequently see their work devalued and find themselves ostracized or excluded from access to important information.”

Although one might expect females to be more supportive of other women, that is frequently not the case. Sixty percent of the senior women interviewed in a Newcastle Business School study reported that senior-level women in their firm do not advocate for other women. Indeed, women often treat their female co-workers more harshly than men do. Especially when there are few women at the top, these so-called queen bees can make it impossible for other qualified women to succeed. As Dr. Peggy Drexler of the Weill Cornell Medical College put it, “[S]ome women are finding their professional lives dominated by high school ‘mean girls’ all grown up: women with something to prove and a precarious sense of security.”

Fortunately, Yale has a number of female and male superstars on the faculty who do actively recruit and support talented women. But more needs to be done. According to the Yale Women Faculty Forum report entitled “Women, Men, and Yale University: A View from 2012,” although the percentage of tenured women at the Yale School of Medicine has grown from 6 percent in 1982–1983 to 22 percent in 2011–2012, only 10 percent of the Yale School of Management tenured faculty are women. In fact, not one woman has been granted tenure at Yale SOM since 2002.

Even when an employer enters the hiring process with the goal of being fair to all candidates, unconscious bias oftentimes gets in the way. That bias has been scientifically measured in recent research conducted at Yale. A 2012 study led by Jo Handelsman, professor of molecular, cellular and developmental biology at Yale, found that biology, chemistry and physics professors at six American universities offered $30,328 to hypothetical male applicants for a position as laboratory manager but only $26,508 to female applicants with identical resumes.

So how do we ensure that employers are indeed hiring and promoting the best candidates? One technique is to emulate the “blind” auditions that are now the norm for hiring musicians for the top American symphony orchestras. Even after orchestras began actively recruiting more female musicians, almost all the orchestra members continued to be males. But once the conductors began auditioning candidates behind a screen, the number of female musicians selected rose dramatically. This suggests that employers can start by removing first names from papers and resumes, just as firms and universities stopped requiring applicants to attach photos.

It is also critical to crack down on sexual stereotyping. As Justice Sandra Day O’Connor wrote in Price Waterhouse v. Hopkins, “An employer who objects to aggressiveness in women but whose positions require this trait places women in an intolerable and impermissible Catch-22: out of a job if they behave aggressively and out of a job if they don’t.” Until employers eliminate this Catch-22, women hoping to emulate Sandburg’s success may find themselves kicked out when they lean in — instead of welcomed into the executive suite or the classroom.

Connie Bagley is a professor at the Yale School of Management. Contact her at connie.bagley@yale.edu.