Performance on a visual discrimination task shows long-term improvement after a single training session. When tested within 24 hr of training, improvement was not observed unless subjects obtained at least 6 hr of posttraining sleep prior to retesting, in which case improvement was proportional to the amount of sleep in excess of 6 hr. For subjects averaging 8 hr of sleep, overnight improvement was proportional to the amount of slow wave sleep (SWS) in the first quarter of the night, as well as the amount of rapid eye movement sleep (REM) in the last quarter. REM during the intervening 4 hr did not appear to contribute to improvement. A two-step process, modeling throughput as the product of the amount of early SWS and late REM, accounts for 80 percent of intersubject variance. These results suggest that, in the case of this visual discrimination task, both SWS and REM are required to consolidate experience-dependent neuronal changes into a form that supports improved task performance.