Although we experience thousands of distinct events on a daily basis, relatively few are committed to memory. The human capacity to intentionally control which events will be remembered has been demonstrated using learning procedures with instructions to purposely avoid committing specific items to memory. In this study, we used a variant of the item-based directed-forgetting procedure and instructed participants to memorize the location of some images but not others on a grid. These instructions were conveyed using a set of auditory cues. Then, during an afternoon nap, we unobtrusively presented a cue that was used to instruct participant to avoid committing the locations of some images to memory. After sleep, memory was worse for to-be-forgotten image locations associated with the presented sound relative to those associated with a sound that was not presented during sleep. We conclude that memory processing during sleep can serve not only to secure memory storage but also to weaken it. Given that intentional suppression may be used to weaken unpleasant memories, such sleep-based strategies may help accelerate treatments for memory-related disorders such as post-traumatic stress disorder.