Sleep plays a key role in the consolidation of newly acquired information and skills into long term memory. Children with Down syndrome (DS) and Williams syndrome (WS) frequently experience sleep problems, abnormal sleep architecture, and difficulties with learning; thus, we predicted that children from these clinical populations would demonstrate impairments in sleep-dependent memory consolidation relative to children with typical development (TD) on a cognitive procedural task: The Tower of Hanoi. Children with DS (n = 17), WS (n = 22) and TD (n = 34) completed the Tower of Hanoi task. They were trained on the task either in the morning or evening, then completed it again following counterbalanced retention intervals of daytime wake and night time sleep. Children with TD and with WS benefitted from sleep for enhanced memory consolidation and improved their performance on the task by reducing the number of moves taken to completion, and by making fewer rule violations. We did not find any large effects of sleep on learning in children with DS, suggesting that these children are not only delayed, but atypical in their learning strategies. Importantly, our findings have implications for educational strategies for all children, specifically considering circadian influences on new learning and the role of children's night time sleep as an aid to learning.