Eureka moments can produce some of the best ideas.

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We don’t always take the “eureka moment,” where somebody is suddenly struck with a brilliant idea, seriously, especially in industries where there is a lot at stake in any given development or product. We tend to think that such ideas, while great for inventors who aren’t under pressure to perform, might be very useful, but when you have to innovate or fail—for example, in the tech industry—constant work seems to be the safe bet.

But a study from Drexel University using word puzzles has found that answers based on insight, on letting the brain do the work unconsciously, are more often correct than answers that come from conscious, analytical thought.

“Conscious, analytic thinking can sometimes be rushed or sloppy, leading to mistakes while solving a problem,” says team member John Kounios, Ph.D, professor at Drexel’s College of Arts and Sciences. “However, insight is unconscious and automatic—it can’t be rushed.”

There are some caveats to this finding, however. For one, insight-based answers take longer. In the study, these eureka moments generally came after the deadline, while answers given just before the deadline were more often wrong. Secondly, insights weren’t always correct and analytical answers weren’t always wrong.

How is this useful to people in the business world? For one, when somebody has a eureka moment, that idea should be taken seriously. Secondly, deadlines can harm both insight- and analysis-based conclusions. Hard deadlines tend to leave teams scrambling to come up with ideas at the last minute, and these ideas are more often than not faulty.

“Deadlines create a subtle—or not so subtle—background feeling of anxiety,” says Kounios. “Anxiety shifts one’s thinking from insightful to analytic. Deadlines are helpful to keep people on task, but if creative ideas are needed, it’s better to have a soft target date. A drop-dead deadline will get results, but they are less likely to be creative results.”

Deadlines are a necessary evil in many industries, but hard deadlines, especially those set as far back as possible and leaving little room for subsequent work, tend to be the most limiting. Consider moving from hard deadlines to soft ones and see if that helps your team generate more eureka moments.