Consolidation makes it possible for memories of our daily experiences to be stored in an enduring way. We propose that memory consolidation depends on the covert reactivation of previously learned material both during sleep and wakefulness. Here we tested whether the operation of covert memory reactivation influences the fundamental selectivity of memory storage--of all the events we experience each day, which will be retained and which forgotten? We systematically manipulated the value of information learned by 60 young subjects; they learned 72 object-location associations while hearing characteristic object sounds, and a number on each object indicated the reward value that could potentially be earned during a future memory test. Recall accuracy declined to a greater extent for low-value than for high-value associations after either a 90 min nap or a 90 min wake interval. Yet, via targeted memory reactivation of half of the low-value associations using the corresponding sounds, these memories were rescued from forgetting. Only cued associations were rescued when sounds were applied during wakefulness, whereas the entire set of low-value associations was rescued from forgetting when the manipulation occurred during sleep. The benefits accrued from presenting corresponding sounds show that covert reactivation is a major factor determining the selectivity of memory consolidation in these circumstances. By extension, covert reactivation may determine the ultimate fate of our memories, though wake and sleep reactivation might play distinct roles in this process, the former helping to strengthen individual, salient memories, and the latter strengthening, while also linking, categorically related memories together.