Even losing an hour's sleep a night can have noticeable effects on a child's mental performance, say scientists.
Children need plenty of sleep, say experts
Researchers at Tel Aviv University in Israel are urging parents not to give in too often to their child's demands for a later bedtime.
They looked at the sleeping habits of 77 children aged between nine and 11, monitoring both the time they went to bed and the number of times they woke up in the night.
They then asked the children to either spend an extra hour asleep for a few nights, or to give up an hour's sleep.
The results, published in were clear-cut - children who got an hour less were significantly more fatigued during the evenings and performed less well at various tests of mental sharpness, which measured reaction times and memory.
Dr Avi Sadeh, who led the study, said: "Previous studies have suggested that children today are getting less and less sleep over the years.
"Parents and childcare professionals can explore the appropriate sleep needs of a specific child by experimenting with extending or restricting sleep, tracking the changes in the child's behaviour and well-being, and finding the child's optimal sleep needs."
I would not allow a child to have a television or computer in their bedroom
Professor Jim Horne, Loughborough Sleep Research Centre
A separate study published in the journal Pediatrics suggested a link between a common sleep disorder and attention deficit hyperactivity disorder (ADHD) in children.
Dr David Gozal of the University of Louisville looked at five to seven year olds diagnosed with mild ADHD symptoms and found that a quarter of them snored - more than might be expected in a non-ADHD group.
This, said Gozal, raised the suggestion that mild sleep apnoea - characterised by breathing difficulties during sleep - might be harming the quality of the children's sleep.
This might be producing symptoms of attention deficit and mild hyperactivity in some of them.
Professor Jim Horne, of the Sleep Research Centre at Loughborough University, told BBC News Online that younger children deprived of sleep tended not to show obvious signs of fatigue, but became hyperactive and irritable.
He said that modern child lifestyles were increasing the risk of sleep deprivation.
He said: "Bedrooms are changing from places of rest and tranquility to places where there are lots of things to keep a child awake, such as computers and televisions.
"I would not allow a child to have a television or computer in their bedroom - or at least place firm limits on their use."