Behavioural sleep problems (childhood insomnias) can cause distress for both parents and children. This paper reports a model describing predictors of high sleep problem scores in a representative population-based random sample survey of non-Aboriginal singleton children born in 1995 and 1996 (1085 girls and 1129 boys) in Western Australia. Longitudinal repeated data were collected up to age 4 years by caregiver report. Children's sleep rhythmicity levels in their first year, as well as conflicted and lax parenting in their second year, predicted higher scores on the sleep problem scale from the Child Behaviour Checklist/2-3 in the children's third year. Higher scores on the sleep problem scale in the children's third year predicted higher scores on the aggressive behaviour subscale of the Child Behaviour Checklist/4-16. The results support a model in which sleep problems mediated the relationship between parental conflict and aggressive behaviour, even when controlling for maternal depression, which has been associated with children's aggressive behaviour. (Contains 5 tables.)