In adults, sleep selectively consolidates those memories that are relevant for future events. The present study tested whether napping after encoding plays a role in selective memory consolidation in infants. Infants aged 15 and 24 months (n = 48 per age) were randomly assigned to a nap or a no-nap demonstration condition, or a baseline control condition. In the demonstration conditions, infants observed an experimenter perform an irrelevant action followed by a relevant action to achieve a desirable outcome on four different toys. Infant imitation of irrelevant and relevant actions was coded at a test session that occurred after a 24-hr delay. The demonstration and test sessions were scheduled around infants’ naturally occurring sleeping patterns. When order of actions was not taken into account, infants in both demonstration conditions exhibited retention of the relevant and irrelevant target actions. Contrary to expectations, infants in the nap condition did not perform the relevant action only more often than infants in the no-nap condition. As expected, only infants in the no-nap condition faithfully reproduced the two actions in the demonstrated order: irrelevant action first, followed by the relevant action. Thus, sleep might help infants to selectively “discard” aspects of a learning experience that they identify as being not useful or relevant in the future.