Most contemporary theories of sensorimotor decision-making formalize the process leading up to a decision as a gradual accumulation of stimulus information over time. In the currently prevailing view, the amount of accumulated evidence required for a decision is independent of the amount of sensory evidence presented by the stimulus, and once that level is reached, a choice is categorically communicated to the motor system to execute an overt response. Recent experiments cast doubt on these assumptions. We adopt a broader perspective by specifying a model with both an evidence and a motor accumulation process. The evidence accumulation signal feeds into a leaky motor accumulator, and it is on the level of the motor accumulation that the final decision criterion is set. We show that this alternative theory describes the behavioral data better, especially when it comes to urgency manipulations, and its neural correlates can be derived from EEG signatures involving systems of both evidence and motor accumulation.