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 6 h later. Thirty-six had a 2 h nap opportunity following learning, while the remaining 18 remained awake throughout. Results showed that, across 6 h 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 associated with fast sleep spindle density during non-rapid eye movement sleep. Moreover, sleep spindles that were coupled to slow oscillations predicted the consolidation of weak memories independently of uncoupled sleep spindles. These relationships were unique to weakly encoded items, with spindles not correlating with memory for intermediate or strong items. This suggests that sleep spindles facilitate memory consolidation, guided in part by memory strength.SIGNIFICANCE STATEMENT Given the countless pieces of information we encode each day, how does the brain select which memories to commit to long-term storage? Sleep is known to aid in memory consolidation, and it appears that certain memories are prioritized to receive this benefit. Here, we found that, compared with staying awake, sleep was associated with better memory for weakly encoded information. This suggests that sleep helps attenuate the forgetting of weak memory traces. Fast sleep spindles, a hallmark oscillation of non-rapid eye movement sleep, mediate consolidation processes. We extend this to show that fast spindles were uniquely associated with the consolidation of weakly encoded memories. This provides new evidence for preferential sleep-based consolidation and elucidates a physiological correlate of this benefit.