Restfulness and recharging can take a back seat to the perception and appearance of productivity. It’s easier to stay on a virtual hamster wheel of activity by immediately responding to every email than it is to measure aggregate productivity over a greater period of time. But a growing field of occupational and psychological research is building the case for restfulness in pursuit of greater productivity.

“Companies are suffering from tremendous productivity problems because people are stressed out” and not recovering from the workday, said Josh Bersin, principal and founder of Bersin by Deloitte. “They’re beginning to realize that this is their problem, and they can’t just say to people, ‘Here’s a work-life balance course, go teach yourself how to manage your inbox,’ ” Mr. Bersin said. “It’s way more complicated than that.”

To be sure, the ability to nap at work is far from widespread, experts said. Few among us have the luxury of being able to step away for a half-hour snoozefest. But lunch hours and coffee breaks can be great times to duck out, and your increased productivity and alertness will be all the evidence you need to make your case to inquiring bosses.

In an ideal world, we’d all solve this problem by unplugging early and getting a good night’s sleep. Here’s our guide on how to do just that. But the next best thing is stealing away for a quick power nap when you’re dragging after lunch.

(The Japanese even have a word for strategically sleeping on the job: “inemuri,” roughly translated to “sleeping while present.” Now is a good moment to pause and email this story to your boss.)