There are more Lord Brownes at the top of major corporations, and they would do well by their firms to come out of the closet.

So says Kirk Snyder, a University of Southern California lecturer who has written about gay executives. Snyder estimates that more than five CEOs at Fortune 500 companies are closeted gays or lesbians. These are apart from Lord John Browne, who recently stepped down from the helm of energy giant BP amid a scandal over his lying in a U.K. court proceeding and a related newspaper story about his relationship with another man.

Executives disclosing their sexual orientation would improve their companies’ reputations in an era when transparency is increasingly valued, Snyder argues.

"I don’t believe that being gay within the majority of Fortune 500 companies is seen as scandalous," Snyder says.

But not everyone agrees it’s a snap for CEOs to disclose a same-sex orientation. Browne’s case is a sign that top corporate leaders continue to face expectations that they be heterosexual, says Jere Keys, communications manager for Out & Equal Workplace Advocates, a San Francisco group that pushes for safe and equitable workplaces for lesbian, gay, bisexual and transgender people. "There’s still an awful lot of pressure to be in the closet," Keys says.

Keys adds, though, that most of that pressure felt by executives "comes from their own perception rather than a hostile workforce or policies."

Indeed, major corporations increasingly have gay-friendly policies. Last year for the first time, the majority of Fortune 500 companies offered domestic partner health insurance benefits, according to a report from advocacy group the Human Rights Campaign Foundation.

Mitchell Gold, co-founder of North Carolina-based furniture firm Mitchell Gold + Bob Williams, has taken a different tack from Browne’s. Gold was openly gay before he and his then-romantic partner Williams started their company in 1989. The pair then gradually made their relationship known to customers and employees. Being gay in a socially conservative community isn’t always easy, but Gold says his disclosure has helped a half-dozen employees come out of the closet and has caused just a handful of workers to quit.

He wishes Browne had revealed his sexual identity sooner without a scandal, in part to show the public that gays can run major firms capably. "It’s a big lost opportunity," he says.

Snyder sees a raft of openly gay and lesbian junior executives who are rising up the corporate ranks. In his book The G Quotient, Snyder found that the leadership style of openly gay men—which generally includes traits such as being more inclusive, adaptable and personally intuitive—tends to be effective at motivating workers and boosting productivity. Closeted gay leaders, his research found, do not show better results.

In addition, Snyder says, closeted corporate leaders risk harming their firm’s good name.

"If I can’t trust someone to tell me the truth about who they are as a human being," he says, "how are you going to trust them about their financial reports or the rest of their business portfolio?"