A new study examines the way chief executives are perceived, and poses the question: Does having a female CEO help or hurt a company’s reputation?

Neither, according to new findings from KRC Research and Weber Shandwick. And that is very good news for women in the C-Suite.

The study, “The Female CEO Reputation Premium? Differences and Similarities,” reported by Fortune magazine, pulls data relating to female CEOs of large companies out of an earlier study. It turns out that CEO reputations, at least in this research, don’t depend on gender.

Approximately the same percentage of respondents at male-run and female-run companies (35 percent and 33 percent, respectively), say their CEO’s reputation is “very strong,” while 38 percent and 36 percent, respectively, say the company’s reputation is “very strong.”

Leslie Gaines-Ross, chief reputation strategist at Weber Shandwick and the study’s author, tells Fortune, “Once you get a woman in the top spot, executives perceive them fairly equally.”

Getting them there is, of course, the hard part.

When it comes to the desire to land in the corner office, the survey turned up some strong discrepancies by gender. Thirty-two percent of men said they aspired to be the top leader of a large company one day, but only 23 percent of women did. That was the global breakdown. When North Americans were asked the same question, the split was even more radical, with 22 percent of men but just 9 percent of women hoping to sit in that corner office.

With more women CEOs of Fortune 500 companies than ever — 23 at Fortune’s last count — what gives? Read the full story at Fortune.com.