Remember all those nights you spent lying awake fretting and counting sheep to try to get to sleep? Of course you do, because counting sheep is a completely useless way of dropping off, scientists have found.

Instead, you should have been dreaming up a mental image of somewhere relaxing, such as a waterfall or a holiday.

Sleep researchers at Oxford University found that those among a group of 50 insomniacs who were told to think of relaxing images fell asleep more than 20 minutes before they normally did, while those who tried "distraction" techniques such as counting sheep fell asleep even later than normal.

Relaxing images push away the worries that keep people awake, suggested Allison Harvey of the department of experimental psychology at Oxford University. "Picturing an engaging scene takes up more brain space than the same dirty old sheep," she told New Scientist magazine. "Plus it's easier to stay with it because it's interesting."

The findings may have widespread usefulness: one in ten people suffers from chronic insomnia, which is reckoned to cost billions of pounds every year in sick days and accidents caused by tiredness.

Dr Harvey made another surprising finding. For years, people have been advised to try to put their worries out of their heads to relax and get to sleep. But a separate study with the group of 50 found that those who tried to suppress their worries took longer to fall asleep than those who let them run their course.

This mirrors the classic psychological study called the "polar bear test" or "elephant test", in which telling someone not to think about polar bears or elephants has the effect of making the image pop unstoppably into the head. So the suppression technique is guaranteed to fail.