During the recent years it has been shown repeatedly that, after initial learning, elapse of time preserves, but sleep enhances performance in procedural motor skills. To date, however, the majority of experimental studies in this area employed some sort of a sequential finger tapping skill as a criterion task. Thus it is unclear yet, if any (and which) other types of motor skills do indeed benefit from sleep. In order to answer this question, and to provide theoretical statements about the memory system regarding benefits of sleep in motor learning, we carried out a series of studies following a "multi-task research strategy". Although we successfully replicated sleep-related improvements in the production of newly acquired sequential finger skills (FT-Task) under different learning conditions (i.e., guided or unguided), we did not find any such effect of sleep in discrete motor tasks requiring precise production of (a) a specific relative timing pattern (Diamond Tapping-Task), or (b) a sub-maximal force impulse (vertical Counter Movement Jump), and we also failed to find any specifically sleep-related effects on subsequent performance in (c) a continuous visuo-motor pursuit-tracking task. These results are considered in relation to other work, and the respective theoretical implications are discussed.