For those who suffer from poor sleep habits, there may be a readily available antidote: plenty of exercise.

It’s no surprise that those who exercise the most and sleep well are among the healthiest of people. Similarly, those with poor sleep and exercise habits are most at risk. But if you’re the type who suffers from insomnia, daytime sleepiness or snoring, exercise can help.

That’s the upshot of findings from scientists in the United Kingdom, who recently published a study showing a synergy between exercise and sleep. In their study, they looked at lifestyle and medical information from nearly 400,000 middle-aged people. Participants documented their normal weekly activity levels as well as information about their sleep quality. Their health was then tracked for an average of 11 years.

Those who were active and had the healthiest sleep scores had these things in common: higher fruit and vegetable consumption, modest alcohol consumption, less time sitting, no shift work, a lack of mental health issues and no smoking.

Overall, the researchers found, a lack of exercise amplified negative outcomes including the effects of poor sleep habits. The least active people were also most at risk of death from stroke, cancer and heart disease.

But for those who struggle with poor sleep, it’s not a lost cause. The scientists noted that 150 minutes of moderate intensity activity or 75 minutes of high intensity activity eliminates most of the negative effects of poor sleep that can lead to death.

While physical activity and improved sleep quality is the true road to improved health, brisk workouts alone can do a body good.