How motor memory consolidates still remains elusive. Consolidation of motor skills has been shown to depend on periods of sleep. Conversely, motor adaptation during tasks not dependent on the hippocampus may not depend on sleep. Some research suggests that the training schedule affects the sleep dependency of motor adaptation tasks. Here, we investigated whether sleep differentially affects memory consolidation that depends on the training schedule. Healthy men were trained with their dominant, right hand on a force-field adaptation task and re-tested after an 11-h consolidation period involving overnight sleep (Sleep) or daytime wakefulness (Wake). Retesting included a transfer test of the non-dominant hand. Half of the subjects in each group adapted to different force-field magnitudes during training with low inter-trial force variability (Sleep-Blocked; Wake-Blocked), and the other half were trained with a high-variability schedule (Sleep-Random; Wake-Random). EEG was recorded during task execution and overnight polysomnography. Consolidation was comparable between Wake and Sleep groups, although performance changes over sleep correlated with sleep spindles nesting in slow-wave upstates. Higher training variability improved retest performance, including transfer learning, and these improvements correlated with higher alpha power in contralateral parietal areas. These enhanced consolidation effects might be fostered by feedback rather than feedforward mechanisms.