Sleep has been shown to be critical for memory consolidation, with some research suggesting that certain memories are prioritized for consolidation. Initial strength of a memory appears to be an important boundary condition in determining which memories are consolidated during sleep. However, the role of consolidation-mediating oscillations, such as sleep spindles and slow oscillations, in this preferential consolidation has not been explored. Here, 54 human participants (76% female) studied pairs of words to three distinct encoding strengths, with recall being tested immediately following learning and again six hours later. Thirty-six had a two-hour nap opportunity following learning, whilst the remaining 18 remained awake throughout. Results showed that across six hours awake, weakly encoded memories deteriorated the fastest. In the nap group however, this effect was attenuated, with forgetting rates equivalent across encoding strengths. Within the nap group, consolidation of weakly encoded items was ass...