Over-imitation has become a well-documented phenomenon. However there is evidence that both social and visible, physically causal factors can influence the occurrence of over-imitation in children. Here we explore the interplay between these two factors, manipulating both task opacity and social information. Four- to 7-year-old children were given either a causally opaque or transparent box, before which they experienced either (1) a condition where they witnessed a taught, knowledgeable person demonstrate an inefficient method and an untaught model demonstrate a more efficient method; or (2) a baseline condition where they witnessed efficient and inefficient methods performed by two untaught models. Results showed that the level of imitation increased with greater task opacity and when children received social information about knowledgeability consequent on teaching, but only for 6- to 7-year-olds. The findings show that children are selectively attuned to both causal and social factors when learning new cultural knowledge.