How do children decide which elements of an action demonstration are important to reproduce in the context of an imitation game? We tested whether selective imitation of a demonstrator’s actions may be based on the same search for relevance that drives adult interpretation of ostensive communication. Three groups of 18-month-old infants were shown a toy animal either hopping or sliding (action style) into a toy house (action outcome), but the communicative relevance of the action style differed depending on the group. For the no prior information group, all the information in the demonstration was new and so equally relevant. However, for infants in the ostensive prior information group, the potential action outcome was already communicated to the infant prior to the main demonstration, rendering the action style more relevant. Infants in the ostensive prior information group imitated the action style significantly more than infants in the no prior information group, suggesting that the relevance manipulation modulated their interpretation of the action demonstration. A further condition (non-ostensive prior information) confirmed that this sensitivity to new information is only present when the ‘old’ information had been communicated, and not when infants discovered this information for themselves. These results indicate that, like adults, human infants expect communication to contain relevant content, and imitate action elements that, relative to their current knowledge state or to the common ground with the demonstrator, is identified as most relevant.