Helping employees quit, and literally paying them a quitting bonus, may seem insane, but many leaders are finding it worthwhile. In my new book, Under New Management, I outline the research which suggests that such incentives might have a positive effect on company performance -- and even on the employees who stay.

In 2009, Amazon acquired Zappos, a quirky and successful online retailer famous for its customer-focused services, culture, and "the offer." During their primary training, new employees are offered $4,000 to leave the company. When Amazon took over, it also acquired "the offer." In his 2014 annual letter to shareholders, Amazon founder Jeff Bezos explained that the company had added a program modeled after the one started by Zappos CEO Tony Hsieh. After some tweaking, Bezos and Amazon aptly titled the program "Pay to Quit."

The program works differently than at  Zappos. Rather than receiving the offer once during training, employees at Amazon's fulfillment centers get the offer once a year, every year. In the first year the offer is for $2,000. The amount then increases by $1,000 each year to a maximum of $5,000, where it remains.

Each year an employee gets the offer, he or she has invested more in the company, and may find it harder to leave. The offer increases to adjust to the sense of investment. For skeptical shareholders, Bezos explained the rationale: "The goal is to encourage folks to take a moment and think about what they really want," he wrote. "In the long-run, an employee staying somewhere they don't want to be isn't healthy for the employee or the company."

Bezos understood that disengaged employees impose financial and emotional costs on an organization, and that even offering $5,000 to help such employees self-select out is a good deal. The real upgrade that Amazon made in the Pay to Quit program over the Zappos program was checking in further along in an employee's tenure and doing so more than just once. In a way, Amazon is asking its employees to give the company a performance evaluation every year. But just as at Zappos, only a small number of employees take the offer -- suggesting that employees are giving the company a pretty good evaluation.

Of course, Bezos wants employees to stay with the company and to be further engaged more than he wants them to quit. In fact, the title of the page that employees read when they receive the offer is "Please Don't Take This Offer." In making the offer every year, Bezos and Amazon achieve greater engagement and productivity, and they rarely even have to pay out $5,000. That's a good deal for all the shareholders, even the ones who might have read the letter skeptically. Gallup's research found that, in 2011-2012, publicly traded companies with 9.3 or more engaged employees for every disengaged employee had 147 percent higher earnings per share than their competitors. Meanwhile, companies with little engagement -- 2.6 engaged employees for every disengaged employee -- had 2 percent less earnings per share than competitors.

If offering cold, hard cash to quit still seems too far out, it's at least worth considering how the principles behind "the offer" can be used in other ways. Any program that provides "a well-lit, safe exit path" would have a similar effect. Processes that encourage employees to examine their reasons for choosing to work for your company are likely to help them reaffirm the wisdom of their original decision, hence engaging further with the organization. In other words, there is more than one way to extend "the offer." And the offer is a good deal.