It is desirable, but not sufficient, that more women become CEOs. Success shattering the glass ceiling must then be followed by success performing the top leadership role. Men can play an important part in achieving that: New research shows that the prospects for female CEOs are greatly improved by an assist from their predecessors, most of whom are male.

The authors of the research, published by the Academy of Management, studied every large company CEO succession between 1989 and 2009 in which a woman assumed the top spot. (The results should hold true for smaller companies as well, the authors say.) For comparative purposes they matched each case with a case involving male succession at a company in the same industry, of a similar size, and in the same year. They defined successful CEOs as those who achieved positive financial results in their first three years on the job.

The authors found that women CEOs do well when they are promoted from within their companies following a long period of grooming by their predecessors. Given the paucity of women atop large companies, those predecessors are, of course, mostly male, although female predecessors likely would have a similar impact. By contrast, male CEOs succeed in similar settings when they are brought in from outside based on their track records, with very short grooming periods.

The actions of the predecessor CEO have an outsize impact on women leaders for two reasons. First, the predecessor has an unmatched opportunity to mentor and sponsor female high-potentials. In the cases studied, the predecessors handpicked their female successors for positions of responsibility and oversaw their professional development. Those successors "have an in-depth intimate knowledge of the firm and its challenges, and the predecessor seems to play a huge role in this," says Priyanka Dwivedi, a management professor at Texas A&M who co-authored the paper.

Second, the predecessor sets the context for a woman's elevation. One reason few women achieve the top role is the pervasive stereotype that CEOs are men. That stereotype can also compromise the ability of a woman to lead if a skeptical workforce doubts her fitness. But to eliminate the stereotype, more women need to reach the top spot and show off their prowess there. "So it is a chicken-and-egg problem," Dwivedi says.

To address that problem, "managing stakeholder expectations is key," says Aparna Joshi, a professor of management at Penn State and another co-author of the paper. The predecessor should promote an inclusive culture throughout the organization and "signal that this woman is a resource worth backing," Joshi says. The CEO's sponsorship of and trust in the female executive as he creates opportunities for her should be visible to the whole organization.

Dwivedi cited as an example Steve Reinemund and Indra Nooyi, the past and present CEOs of PepsiCo. Reinemund "proclaimed that [Nooyi] needed to partner with him while he was CEO," she says. "He was indicating five years before the succession that she was the chosen one."

CEOs who remain active on their companies boards' continue to affect the performance of their female successors, but in less consistent ways. In many smaller organizations and industries that aren't heavily male, the ongoing advisory role is beneficial. But "in male-dominated industries and in larger organizations, women were more successful when the predecessor was not around," Dwivedi says. "So the female CEO inherited power and authority completely."

The authors say that current CEOs who understand their potential to influence the performance of a female successor should replicate those practices. "We often ask what women can do" to increase their numbers in the corner office, Joshi says. "Women have made extraordinary gains in education, in human capital, in every domain. I think it is now up the organizational leaders to act."