Sleep is a vital need, forcing us to spend a large portion of our life unable to interact with the external world. Current models interpret such extreme vulnerability as the price to pay for optimal learning. Sleep would limit external interferences on memory consolidation1–3 and allow neural systems to reset through synaptic downscaling4. Yet, the sleeping brain continues generating neural responses to external events5,6, revealing the preservation of cognitive processes ranging from the recognition of familiar stimuli to the formation of new memory representations7–15. Why would sleepers continue processing external events and yet remain unresponsive? Here we hypothesized that sleepers enter a ‘standby mode’ in which they continue tracking relevant signals, finely balancing the need to stay inward for memory consolidation with the ability to rapidly awake when necessary. Using electroencephalography to reconstruct competing streams in a multitalker environment16, we demonstrate that the sleeping brain amplifies meaningful speech compared to irrelevant signals. However, the amplification of relevant stimuli was transient and vanished during deep sleep. The effect of sleep depth could be traced back to specific oscillations, with K-complexes promoting relevant information in light sleep, whereas slow waves actively suppress relevant signals in deep sleep. Thus, the selection of relevant stimuli continues to operate during sleep but is strongly modulated by specific brain rhythms.