Memory consolidation benefits from sleep. In addition to strengthening some memory traces, another crucial, albeit overlooked, function of memory is to erase irrelevant information. Directed forgetting is an experimental approach consisting in presenting "to be remembered" and "to be forgotten" information that allows selectively decreasing or increasing the strength of individual memory traces according to the instruction provided at learning. This paradigm was used in combination with functional MRI to determine, in humans, what specifically triggers at encoding sleep-dependent compared with time-dependent consolidation. Our data indicate that relevant items that subjects strived to memorize are consolidated during sleep to a greater extent than items that participants did not intend to learn. This process appears to depend on a differential activation of the hippocampus at encoding, which acts as a signal for the offline reprocessing of relevant memories during postlearning sleep episodes.