Recent research has revealed a striking tendency in young children to imitate even causally irrelevant actions, a phenomenon dubbed ‘over-imitation’. To investigate whether children develop beyond this, we allowed both adults and children to witness either a child or adult model performing goal-relevant and goal-irrelevant actions to extract a reward from a transparent puzzle box. Surprisingly, copying of irrelevant actions increased with age, with the adults performing the task with less efficiency than the children. Participants of all ages were more likely to perform the irrelevant actions performed by an adult model, than by a child model. These results suggest that people may become more imitative as they mature, whilst selectively copying particular models with a high level of fidelity. We suggest that this combination of faithful copying and selectivity underwrites the powerful social learning necessary for the level of cultural transmission on which our species depends.