You probably already know how important sleep is to your health and general well-being. You may even know that you need deep sleep every night to clear out the toxins that lead to Alzheimer's. But if you're running a company or managing a business, or just have a lot of work to do, it may seem to you that there's a tradeoff between getting as much sleep as you know you need and doing all the work that you need to get done. At least, I often feel that way.

It turns out that's the wrong way to look at it because scientific research shows exactly how much we suck at our jobs when we don't get plenty of sleep--at least seven hours a night and ideally eight-and-a-half hours. So it really isn't a tradeoff between getting enough sleep and getting the important stuff done.

There's a small but growing group of readers who get a daily text from me with a self-care or motivational micro-challenge or idea. Often they text me back and we wind up in an ongoing conversation. (Interested in joining? You can learn more here.) Many are entrepreneurs, solopreneurs, or authors, and they tell me that getting at least seven to eight hours of sleep a night is essential for their ability to function and their continued success.

Some recent experiments show why that is, as physician Austin Perlmutter explains in a fascinating article on the Psychology Today website. Here are some scientifically demonstrated ways that not getting enough sleep can affect you as a leader.

1. You can't focus.

A series of experiments at Washington State University in Spokane showed that participants who haven't had enough sleep performed poorly on the Psychomotor Vigilance Test, a simple 10-minute test in which subjects must push a button every time a light turns on and that is widely used to measure the effects of sleep deprivation. Not surprisingly, researchers found that participants who'd been kept awake for 62 hours performed very badly on the test. But they also restricted some participants' time in bed to six hours a night over two weeks. Those participants' performance also suffered--even though they didn't feel particularly sleepy. Keep these findings in mind if you think you're just fine on six hours of sleep a night.

2. Your judgment may be off.

In another experiment at the University of L'Aquila in Italy, 42 subjects were restricted to five hours of sleep a night for five nights. Then the subjects were shown 90 images designed to elicit emotional responses that were positive, negative, or neutral. The subjects consistently viewed the negative images in a negative way. But when they were sleep deprived, they also viewed the positive and neutral images more negatively than when saw those images after plenty of sleep. This wasn't just a matter of tiredness making people grumpy because the effect was the same even when participants were in a good mood.

For a business leader, the implications are obvious, and they should scare you. If five nights without enough sleep can make you think, say, that a piece of good news is really bad news, imagine how weeks or months of insufficient sleep might affect your ability to make good decisions.

3. You can't solve tough problems.

Researchers have long explored the association between creativity and dreams. And of course, many of today's most famous creations, including the Beatles song "Yesterday" and the algorithm for Google's search engine, came to their creators in dreams. Creativity is essential for problem-solving and researchers have long suspected that the lack of both REM (dreaming) sleep and deep sleep can hamper your creativity.

It can definitely impede your ability to solve difficult problems. Researchers at Lancaster University in England gave a series of problems, varying in difficulty, to 63 subjects. As expected, they were able to solve some of these problems, but not others. Subjects were given the chance to try again, either immediately, a few hours later, or after a good night's sleep. Those who had slept were better able than the others to solve tough problems that had stumped them the day before.

Are focus, good judgment, and the ability to solve difficult problems necessary in your job? I'm guessing your answer is yes. So next time you decide to skimp on sleep because there's a task you just have to get done or a meeting you really must attend, stop for a moment and consider what you're giving up. It might be something even more important.