Human sleep is a global state whose functions remain unclear. During much of sleep, cortical neurons undergo slow oscillations in membrane potential, which appear in electroencephalograms as slow wave activity (SWA) of <4 Hz. The amount of SWA is homeostatically regulated, increasing after wakefulness and returning to baseline during sleep. It has been suggested that SWA homeostasis may reflect synaptic changes underlying a cellular need for sleep. If this were so, inducing local synaptic changes should induce local SWA changes, and these should benefit neural function. Here we show that sleep homeostasis indeed has a local component, which can be triggered by a learning task involving specific brain regions. Furthermore, we show that the local increase in SWA after learning correlates with improved performance of the task after sleep. Thus, sleep homeostasis can be induced on a local level and can benefit performance.