Milwaukee ? Please, please accept a high-paying job with us. In fact, just swing by for an interview and we’ll give you a chance to win cash and prizes.

Sounds too good to be true, especially in an economy riddled with job cuts in nearly every industry. But applicants for nursing jobs are still so scarce that recruiters have been forced to get increasingly inventive.

One Michigan company literally rolled out a red carpet at a recent hiring event. Residential Home Health, which provides in-home nursing for seniors on Medicare, lavished registered nurses and other health care workers with free champagne and a trivia contest hosted by game-show veteran Chuck Woolery. Prizes included a one-year lease for a 2009 SUV, hotel stays and dinners.

The long-standing U.S. nurse shortage has led to chronic understaffing that can threaten patient care and nurses’ job satisfaction.