•Cultural evolution theory posits selective copying, but children over-imitate.•Here we show that 4- to 6-year-old children selectively copy a majority.•They only imitate their irrelevant actions when observers approved of them.•Children do not blindly follow the crowd: they are broadly optimal imitators.•This selective and flexible learning provides the basis for cumulative culture. Cultural evolutionary theory posits that human cultural complexity rests on a set of adaptive learning biases that help to guide functionality and optimality in social learning, but this sits in contrast with the commonly held view that children are unselective “over-imitators.” Here, we tested whether 4- and 6-year-old children use social learning biases flexibly to fine-tune their copying of irrelevant actions. Children watched a video of a majority demonstrating causally irrelevant actions and a minority demonstrating only causally relevant actions. In one condition observers approved of the majority and disapproved of the minority, and in the other condition observers watched the majority and minority neutrally. Results showed that both 4- and 6-year-olds copied the inefficient majority more often than the efficient minority when the observers had approved of the majority’s actions, but they copied the efficient minority significantly more when the observers had watched neutrally. We discuss the implications of children’s optimal selectivity in copying and the importance of integrating social approval into majority-biased learning when acquiring norms and conventions and in broader processes of cultural evolution.