The interactive race model of saccadic countermanding assumes that response inhibition results from an interaction between a go unit, identified with gaze-shifting neurons, and a stop unit, identified with gaze-holding neurons, in which activation of the stop unit inhibits the growth of activation in the go unit to prevent it from reaching threshold. The interactive race model accounts for behavioral data and predicts physiological data in monkeys performing the stop-signal task. We propose an alternative model that assumes that response inhibition results from blocking the input to the go unit. We show that the blocked-input model accounts for behavioral data as accurately as the original interactive race model and predicts aspects of the physiological data more accurately. We extend the models to address the steady-state fixation period before the go stimulus is presented and find that the blocked-input model fits better than the interactive race model. We consider a model in which fixation activity is boosted when a stop signal occurs and find that it fits as well as the blocked input model but predicts very high steady-state fixation activity after the response is inhibited. We discuss the alternative linking propositions that connect computational models to neural mechanisms, the lessons to be learned from model mimicry, and generalization from countermanding saccades to countermanding other kinds of responses.