Ask a business leader the secret of his success and he will reach into his humility bag and extract one of the following:

'I was lucky.'

'I fake it till I make it.'

'I hire people who are smarter than I am.'

The first two explanations, of course, are rhetorical packing peanuts. But the third is a more-or-less sincere shout-out to a dedicated team. It is also—usually—the speaker's actual practice. I say 'usually' because leaders don't always pant after A-players. Specifically, they may not like superstars who challenge them in their own core competencies.

Hence: a founder whose genius is sales may squirm in the presence of a superior closer. A leader who considers herself inventor-in-chief may resent the R&D head who is a fount of ingenious product ideas. The CEO who calls communications his greatest gift may go squint-eyed when a member of his executive team wields a suppler tongue or pen.

Bosses are most threatened by underlings who seem more intelligent than they are. Shrewd applicants show off their brains during job interviews, but pull their intellectual punches if they sense their supervisor-to-be functions on a less-exalted plane. They treat the conversation like a treadmill: maintaining a speed at which the leader works up a slight sweat but never grows winded. Unaware that he is being patronized, the boss feels challenged but not threatened.

I have seen this scenario play out in two ways. In the first, the cerebral one—once safely ensconced—lifts the bushel, removes her light, and proceeds to dazzle her new colleagues. The CEO, unhappy at having rings run round him in public, starts to bristle. At which point the hire pares back her contributions in meetings and steps gingerly for fear of trampling the leader's ego. In private conversations, however, she cogently dissects the boss's every inadequacy and error. She may or may not be correct (the CEO, after all, knows his company best). But her arguments are so articulate and persuasive that doubt is sowed and loyalty undermined. And of course the CEO fails to derive full value from her abundant talents.

Alternatively, the leader accepts his subordinate's superior intellect—even revels in it. He sees her presence as an opportunity to dream bigger: charging her with projects he might have felt inadequate to take on himself and encouraging others' loyalty to her (while emphasizing that it translates into loyalty to him). In interactions with the outside world, he concludes that hers is sometimes the company's best face. He may even, on occasion, allow her to delegate to him.

And he reminds staff that his underling's brilliance reflects well on his own ability to identify and land talent. That will be comforting if he finds himself substantially eclipsed. More important, it sets the standard for managers who handle hiring at lower levels. Unlike the CEO, they may worry about bringing on prodigies who could pinch their jobs. They must learn that the recruitment of genius is a kind of genius in itself.