Memories are enhanced during sleep through memory consolidation processes. A recent study reported that sleep increases competitive forgetting in the absence of sleep-dependent consolidation of the target memory (Racsmany et al. in Psychol Sci 21:80-85, 2010). Here, using a modified retrieval-induced forgetting task, we examined whether sleep-dependent modulation of forgetting occurs concurrently with the consolidation of related target memories. Participants encoded a word-pair list and then practiced retrieving a portion of these pairs. Following a break with sleep or wake, recall of all pairs was tested. As expected, recall for practiced pairs was greater following sleep relative to wake. Contrary to Racsmany et al. (Psychol Sci 21:80-85, 2010), competitive forgetting decreased following sleep. Moreover, recall for practiced pairs correlated with slow wave sleep (SWS) while forgetting of competing targets correlated negatively with REM, suggesting a novel function of these sequential brain states on memory processing.