If a CEO position stays open for too long, it could indicate a couple of things, none of them all that promising to a potential candidate.

Sears had an “interim” CEO for three years, until Lou D’Ambrosio took over this past May. Lloyds Bank (LYG) CEO António Horta-Osório recently stepped down claiming it was on account of chronic fatigue, and the company’s interim CEO, Tim Tookey, plans to leave at the beginning of 2012. If Horta-Osório doesn’t feel better, Lloyds will bring on a replacement interim, CEO David Roberts.

Time Inc., a division of Time Warner (TWX) (and Fortune’s parent company), is no stranger to this problem. An “interim management committee” has been running the ship at the magazine publisher for the past nine months and a replacement, Digitas CEO Laura Lang, was announced last week.

Investors get restless about these types of management gaps, and for good reason. For one, lag time between CEOs can indicate a problem with leadership development within a company, says Sydney Finkelstein, a professor of management at Dartmouth’s Tuck Executive Education School.

Unsurprisingly, companies with clear succession plans can sidestep leadership blips. CEOs who keep a close watch on talent rising through the ranks tend to have a good sense of the ideal candidates, Finkelstein says. Organizations that have an HR person in their C-suite also tend to prioritize leadership development.

But sometimes companies need fresh eyes and must hire outside. If that’s the case, they should steer clear of a purely self-promotional pitch to CEO candidates, says Mark Jaffe, president of executive search firm Wyatt and Jaffe. “I think we’ve reached a point where companies need to be a little bit more transparent, not only with their shareholder constituency, but with the talent they are trying to attract.”

That can be a tough sell when a company has serious problems. Sales at Sears (SHLD), for example, fell every year since Eddie Lampert combined the company with K-Mart in 2005. Lloyds Banking Group is navigating a sale of over 600 branches to start to pay the government back for its bailout.

So you can’t blame executives if they aren’t breaking down the door to get to a corner office at a troubled company. But honesty is critical in the interview process, Jaffe says, even if the truth hurts. “Sometimes I’ll say, ‘Look, you may be buying a ticket on the Titanic here, but you will have a first-class suite,’” he says. “You have to have a little bit of humility and a sense of humor and a willingness to be realistic….”

Companies that are upfront about their problems show that they know their strengths and weaknesses. That kind of self-knowledge might sound simple, but it is actually a critical first step. Besides, an honest, thorough self-assessment may lead some organizations to think more creatively about who their ideal leader might be. “There is a small club of about 40 50-year-old men with fabulous hair that are considered to be the diamond-cutters,” Jaffe says, “but it’s all smoke and mirrors.”

Companies in recruiting mode could actually benefit from looking beyond the typical talent pool. Not that there are hundreds of unknowns waiting in the wings to turn Sears around, Jaffe says, but “it’s very possible to take a different view of an executive’s performance and come up with a whole different kind of list of people who do extraordinary things.”

Understandably, businesses that are facing problems usually play it safe and make more conservative CEO hires. But in some situations, the best choice is to go after someone cheaper, hungrier, and possibly a little further from the limelight than the usual suspects. And who knows, he or she could be the next big name that everybody wants.