I have met CEOs without vision. I have met CEOs without ethics. I have met CEOs without people skills, senses of humor, or a proper aversion to suspenders. But I have never met a CEO without an open-door policy.

"Something there is that doesn't love a wall," wrote Robert Frost, and that same antipathy applies to doors--at least in the human-capital-hugging world of business. Wary of appearing autocratic or uncaring, leaders bend over backward to be accessible. And hooray for that, because isolation is among the greatest threats to those at the top. Employees need and want to talk to you. They come seeking clarification, inspiration, reality checks. They also come bearing intelligence, some of which you might not otherwise hear. And an open door suggests an open mind. I value your perspective, it suggests. Or simply: I value your company.

But with deadlines that need meeting and big thoughts that need thinking, workplace reality subverts the rhetoric of invitation. CEOs say people are their most important asset, but not every task is advanced through conversation. And--let's face it--time spent with some people is time you'll never get back. Thus arises the disjuncture of words and actions. "Ideas? Problems? My door is always open," says the CEO, before disappearing behind a slab of oak. Employees wandering past can't help feeling excluded, and maybe a little unnerved. ("Who is she talking to? Why is she hiding? This can't be good.…")

Employees also wrestle with the open-and-shut question, fearful both of having their time wasted and of being labeled antisocial. Their choices influence company culture. Hallways lined with closed doors can seem sinister, secretive, or depressing. Conversely, when everyone leaves doors ajar, noise levels rise and productivity suffers. Open-door environments also encourage serial perambulators, employees who constantly stroll around in search of a chat.

One CEO who has the open-door problem licked is David Mammano, founder of Next Step Publishing, which produces magazines for high school students. For years, "people would think, 'If I close my door I'm going to send a bad message.' They'd leave it open and someone would walk in and blah, blah, blah," says Mammano. His solution: Buy everyone loofahs shaped like feet (Next Step's logo includes a foot) to hang on their closed doors or outside their cubicles for one hour a day. During that hour "no one can interrupt you unless the place is burning down," says Mammano. The feet acknowledge that people sometimes need privacy. At the same time, the one-hour limit precludes hermitlike proclivities.

Of course, CEOs may need more than an hour of "me" time, and so Mammano schedules one Friday a month in which he escapes to a library or coffee shop to read and work and think big thoughts. "I call it 'Dave's Top of the Mountain Day," he says. "There are no distractions. I have the peace to get deep into my cerebral cortex."

Meanwhile, employees who peer into the boss's empty office know where he is and why. And no one feels offended.

Leigh Buchanan is an Inc. editor-at-large.