Two different experimental paradigms are used to measure reaction time (RT) to a crossmodal stimulus set. In the redundant target (aka divided-attention) paradigm, stimuli from different modalities are presented simultaneously or with certain stimulus onset asynchrony (SOA), and the participant is instructed to respond to the stimulus detected first. Typically, the time to respond in the crossmodal condition is faster than in either of the unimodal conditions. In the focused attention paradigm, crossmodal stimulus sets are presented in the same manner but now, participants are instructed to respond only to the onset of a stimulus from a specifically defined target modality, such as the visual, and to ignore the remaining non-target stimulus, the tactile or the auditory, say. In the latter setting, when a stimulus of a non-target modality, a tone, say, appears before the visual target, there is no overt response to the tone if the participant is following the task instructions. Nevertheless, the non-target stimulus has been shown to modulate the saccadic response to the target. The distinction between the redundant target and the focused attention paradigm is not only an interesting experimental variation as such, but it may also provide an important theoretical perspective. In fact, since the stimulus setup can be chosen to be identical in both paradigms, any differences observed in the responses would have to be due to the instructions only. Here we show how the time-window-of-integration (TWIN) model developed by the authors (Colonius & Diederich, JCogNeurosci 2004; Diederich & Colonius, BrainRes 2008) accounts for such results.