Across-trial variability of EEG decreases more markedly before self-initiated than before externally triggered actions, providing a novel neural precursor for volitional action. However, it remains unclear whether this neural convergence is an early, deliberative stage or a late, execution-related stage in the chain of cognitive processes that transform intentions to actions. We report two experiments addressing these questions. Participants viewed randomly moving dots on a screen. At a random time, all dots started moving coherently to the left or right side of the screen. Participants were rewarded for correctly responding to the direction of coherent dot movement. However, the waiting time before coherent dot motion onset could be extremely long. Participants had the option to skip waiting by pressing a “