The study looked at children aged seven or eight
A good night's sleep could reduce hyperactivity and bad behaviour among children, a Finnish study reports.
It has been suggested that some children who lack sleep do not appear tired, but instead behave badly.
Of the 280 examined in the Pediatrics study, those who slept for fewer than eight hours were the most hyperactive.
Experts said adequate sleep could improve behaviour in healthy children and reduce symptoms of attention deficit hyperactivity disorder (ADHD).
It is recognised that chronic sleep deprivation is a problem for many adults in Western countries and that it can have consequences for their health and daily life.
The team behind this research said not enough was understood about the role of sleep in children's lives but it has been estimated that a third of US children do not get enough sleep.
In this research, the team from the University of Helsinki and Finland's National Institute of Health and Welfare studied 280 healthy children aged seven or eight.
They wanted to see if those healthy children who slept the least were the most likely to display the kind of symptoms associated with ADHD.
None of the children studied had the attention disorder.
Parents filled in questionnaires about their children's usual sleeping habits and then noted how long their children slept for over seven nights.
The children also wore devices called actigraphs, which measure movement, to monitor how long they actually rested for.
Parents' estimates of sleep duration were longer than the actigraph measurements, which the researchers say could be because they measured from bedtime or because they assumed their children were asleep when they were simply lying awake in bed or reading.
The parents were also asked about their children's behaviour, using measures normally used to diagnose ADHD.
The children whose average sleep duration as measured by actigraphs was shorter than 7.7 hours had a higher hyperactivity and impulsive behaviour score.
They also had a higher ADHD symptom score overall.
'Sleep needs differ'
Dr Juulia Paavonen, who led the study, said: "We were able to show that short sleep duration and sleeping difficulties are related to behavioural symptoms of ADHD.
"The findings suggest that maintaining adequate sleep schedules among children is likely to be important in preventing behavioural symptoms.
"It may well be that inadequate sleep is increasing some of the behavioural problems that have been seen in children with attention deficit disorders."
Dr Paavonen said further studies were needed to confirm the link.
And she advised parents that, even though the study suggested fewer than eight hours sleep could be problematic, it was not a figure everyone should aim for.
"Sleep needs differ between individuals. The only way to take care that a particular child has enough sleep is to see if they seem to have a problem with short sleep.
"But even [an extra] 30 minutes per night has been shown to give a major improvement in objective cognitive tests, improving reaction times, impulsivity and attention spans."
Sleep expert Neil Stanley, of the University of East Anglia, said: "It has been acknowledged for a while now that there is a lot of commonality between the symptoms of a tired child and the symptoms of a child with ADHD."
He said parents needed to recognise that sleep was important for children.
"These things have been lost at a time when ADHD is increasing.
"How much of what is diagnosed as ADHD is something that can be modified or improved, or even totally cured by a more rigid sleep pattern?
"Maybe parents should try and get sleep sorted out. If the child is still showing symptoms, then that's probably the time to look at pharmacological interventions."