Dr. David Dinges, a sleep researcher at the University of Pennsylvania, is a strong advocate of prophylactic napping—taking what he and others call a "power nap" during the day to head off the cumulative effects of sleep loss.

Daytime napping can also help repay a sleep debt, and some experts even suggest that a two-hour "prophylactic nap" early in a long, planned period of sleep deprivation can help maintain productivity.

"To search for effective strategies, such as napping, that permit work while minimizing the effects of sleepiness is consistent with good planning and management." Not only that, but once an employee has decided he needs to doze, it will be best for everyone if he puts his head down as soon as possible.

This the researchers call a prophylactic nap. Be prophylactic, they say. Delay your doze and productivity will plummet.