Efficient cognitive decisions should be adjustable to incoming novel information. However, most current models of decision making have so far neglected any potential interaction between intentional and stimulus-driven decisions. We report here behavioral results and a new model on the interaction between a perceptual decision and non-predictable novel information. We asked participants to anticipate their response to an external stimulus and presented this stimulus with variable delay. Participants were clearly able to adjust their initial decision to the new stimulus if this latter appeared sufficiently early. To account for these results, we present a two-stage model in which two systems, an intentional and a stimulus-driven, interact only in the second stage. In the first stage of the model, the intentional and stimulus-driven processes race independently to reach a transition threshold between the two stages. The model can also account for results of a second experiment where a response bias is introduced. Our model is consistent with some physiological results that indicate that both parallel and interactive processing take place between intentional and stimulus-driven information. It emphasizes that in natural conditions, both types of processing are important and it helps pinpoint the transition between parallel and interactive processing.