Under standard imitation dynamics, the strategy Defect is known to be stable to invasion against Cooperate in the spatial Prisoner's Dilemma game. We show that when imitation is based on a 'bank' or sum of all payoffs up to time t, Defect is no longer stable. We study dynamics for the single invader and random initial strategy cases, finding that for large enough initial bank values, cooperation not only persists but can dominate the domain.