(FORTUNE Magazine) – Suppose that your job were to open up today, and that you applied for it. Would you get it? Why--or why not? For years some executive coaches have been asking their clients to answer those questions as part of a candid self-assessment. Lately, though, what I'm hearing from readers is that employers are turning a hypothetical exercise into a test with teeth. "My company recently restructured following a merger, and all of us middle and senior managers are now required to reinterview [with the new management] to be 'hired,' " writes a department head at a FORTUNE 500 company. "I want to make a lateral move to a new position on the organization chart, but I know that several other candidates (both internal and external) are vying for it. How do I stand out from the crowd?"

If ever there were a time to learn the subtle science of self-promotion, this is it--and not only for people whose careers are being buffeted by restructurings. "It's stunning to me how many people think that if they keep their heads down and work hard, their boss 'will just know' what they're contributing and how valuable they are, as if there were some kind of psychic connection there," says Peggy Klaus, a communications guru who has coached executives at J.P. Morgan Chase, American Express, Disney, and Goldman Sachs, among other places. You mean there's not? "You have to let the people above you know what you're doing, what skills you're developing, which goals you're achieving," advises Klaus, who is also the author of Brag!: The Art of Tooting Your Own Horn Without Blowing It ($24.95, Warner Business Books). "Don't make them guess."

Clearly, if you have a whole new management team to impress, bragging is even more crucial than usual. But how to do it without turning into one of those people whom colleagues will duck into the nearest broom closet to avoid? "The more specific details you give, the clearer your achievements will be to people who don't know you well. But don't spout off a laundry list of items beginning with 'I.' That's just boring. Instead, practice talking about your accomplishments gracefully, by weaving them into a story," suggests Klaus. Then practice telling your story until it comes naturally. To get you started, Klaus devised a 12-item checklist of possible talking points (in her book or at www.bragbetter.com), including, How does your job use your skills and talents, and what projects are you working on right now that best showcase them? What career successes are you most proud of? What skills have you picked up in the past year?

It's no use counting on anyone else to tell the big cheeses how great you are, says Klaus: "Your boss is probably too worried about his or her own future to be taking much care of yours." One last tip: "Listen. Ask the new management team what they hope to accomplish." The point here, naturally, is to suggest ways that you could help out. But at the same time, notes Klaus, "showing a genuine interest in other people's goals really floors them." Why? "They're just not used to it."