Diverse psychophysical and neurophysiological results show that oculomotor networks are continuously active, such that plans for making the next eye movement are always ongoing. So, when new visual information arrives unexpectedly, how are those plans affected? At what point can the new information start guiding an eye movement, and how? Here, based on modeling and simulation results, we make two observations that are relevant to these questions. First, we note that many experiments, including those investigating the phenomenon known as "saccadic inhibition", are consistent with the idea that sudden-onset stimuli briefly interrupt the gradual rise in neural activity associated with the preparation of an impending saccade. And second, we show that this stimulus-driven interruption is functionally adaptive, but only if perception is fast. In that case, putting on hold an ongoing saccade plan toward location A allows the oculomotor system to initiate a concurrent, alternative plan toward location B (where a stimulus just appeared), deliberate (briefly) on the priority of each target, and determine which plan should continue. Based on physiological data, we estimate that the advantage of this strategy, relative to one in which any plan once initiated must be completed, is of several tens of milliseconds per saccade.