A gradual buildup of neuronal activity known as the "readiness potential" reliably precedes voluntary self-initiated movements, in the average time locked to movement onset. This buildup is presumed to reflect the final stages of planning and preparation for movement. Here we present a different interpretation of the premovement buildup. We used a leaky stochastic accumulator to model the neural decision of "when" to move in a task where there is no specific temporal cue, but only a general imperative to produce a movement after an unspecified delay on the order of several seconds. According to our model, when the imperative to produce a movement is weak, the precise moment at which the decision threshold is crossed leading to movement is largely determined by spontaneous subthreshold fluctuations in neuronal activity. Time locking to movement onset ensures that these fluctuations appear in the average as a gradual exponential-looking increase in neuronal activity. Our model accounts for the behavioral and electroencephalography data recorded from human subjects performing the task and also makes a specific prediction that we confirmed in a second electroencephalography experiment: Fast responses to temporally unpredictable interruptions should be preceded by a slow negative-going voltage deflection beginning well before the interruption itself, even when the subject was not preparing to move at that particular moment.