In addition to performance gains accrued concurrently with a given training experience (within-session gains) robust, delayed (between-session) performance gains may slowly evolve in the absence of any additional practice in a variety of tasks. The latter is regarded as a behavioral manifestation of skill memory consolidation. It is not known, however, how much practice is necessary for the triggering of these consolidation effects. Here, using an enumeration task, we show that the triggering of delayed gains could be robustly predicted from each individual's performance curve. Delayed performance gains evolved consistently only when practice continued to the point at which within-session performance leveled off (saturation). No delayed gains were found when training was stopped before this individually determined point. Our results support the notion that the triggering of consolidation processes depends on the saturation of a distinct, early phase of learning rather than on the absolute number of task repetitions, and suggest the possibility that training and rehabilitation protocols could be optimized on an individual basis.