Background: Solving a task with insight has been associated with occipital and right-hemisphere activations. The present study tested the hypothesis if sleep-related alterations in functional activation states modulate the probability of insight into a hidden abstract regularity of a task. Methodology: State-dependent functional activation was measured by beta and alpha electroencephalographic (EEG) activity and spatial synchronization. Task-dependent functional activation was assessed by slow cortical potentials (SPs). EEG parameters during the performance of the Number Reduction Task (NRT) were compared between before sleep and after sleep sessions. In two different groups, the relevant sleep occurred either in the first or in the second half of the night, dominated by slow wave sleep (SWS) or by rapid eye movement (REM) sleep. Principal Findings: Changes in EEG parameters only occurred in the early-night group, not in the late-night group and indicated occipital and right-hemisphere functional alterations. These changes were associated with off-line consolidation of implicit task representations and with the amount of SWS but they did not predict subsequent insight. The gain of insight was, however, independently associated with changes of spectral beta and alpha measures only in those subjects from the two sleep groups who would subsequently comprehend the hidden regularity of the task. Insight-related enhancement of right frontal asymmetry after sleep did not depend on sleep stages. Significance:It is concluded that off-line restructuring of implicit information during sleep is accompanied by alterations of functional activation states after sleep. This mechanism is promoted by SWS but not by REM sleep and may contribute to attaining insight after sleep. Original neurophysiologic evidence is provided for alterations of the functional activation brain states after sleep. These alterations are associated with a decrease in controlled processing within the visual system and with an increase in the functional connectivity of the right hemisphere, and are supported by SWS in the first half of the night.