Got a stubborn work problem that needs some brainstorming, or a puzzling riddle that requires some creative insight? Tackle it when you are sleepy. This answer seems counterintuitive—surely feats of mental dexterity require the focus that comes from an alert mind. But when it comes to creative tasks, fatigue is your friend.

Ron Friedman, author of the book The Best Place to Work, explains why in "HBR Ideacast," a podcast from Harvard Business Review (via New York):

[I]t’s partly because, in order to be creative, sometimes you need to consider some ideas that don’t necessarily feel like they’re on track with what you're trying to achieve. And so having all these ideas come into your mind because you’re not quite as good at putting them off when you're tired can actually make you more creative.

This effect makes tired people better at solving problems that require insight. That’s also why grabbing a cup of coffee isn’t always the best way to seek eureka moments. The focus caffeine lends can get in the way of those stray thoughts. Maybe that’s also why messy desks often go hand in hand with a creative mind—the clutter could be stimulating.

Sciences supports these suspicions. For the Atlantic, Olga Khazan writes about a study led by Marieke Wieth, a psychology professor at Albion University. Wieth posed insight-based and analytical problems to more than 400 students at different times of the day. The team also classified the students as night owls or morning larks. They found no difference in how well the students preformed on analytical problems (which were akin to the math questions you might find on the SAT). But the students did better on the insight problems when they were less awake.

Friedman suggests that workers schedule creative tasks during their mid-afternoon slow-down or first thing in the morning—depending on when the brain fog most commonly descends. It may not seem pleasant, but it could get you farther in the long run.

Of course, this work can only take us so far: No one has suggested that you do your work anything other than sober, despite the finding that alcohol can also lubricate the creative mind.