Rotating shifts have something to do with the large number of police officers with sleep problems. Working days one week and nights the next can scramble anyone's sleep. But Czeisler says that's not the only cause.

"The single greatest risk factor for obstructive sleep apnea is obesity. And in fact we found that four out of five police officers were overweight or obese."

One of the agencies in this study, the Massachusetts State Police, had much lower rates of obstructive sleep apnea. Their cops also had a significantly lower rate of obesity than other officers in the study. Czeisler says Massachusetts required its state troopers to pass a fitness test, and equipped each police barracks with a fitness center.

"They also made it a requirement that every state trooper spend an hour exercising on each one of their shifts. And that was paid time to work out in those gym facilities."