Analyzing RT distributions in the Simon task reveals that congruency effects decrease for the longest RTs. Four experiments were carried out to examine whether this decrease of the congruency effect with response speed was under a top-down control or due to bottom-up mechanisms. We specifically manipulated the availability of attentional resources by requiring participants to perform a Simon task concurrently to different secondary tasks. RT distribution analysis (in particular delta functions) was performed under both single-task and dual-task conditions. Results show that the reduction of the interference effect with time could be affected when the Simon task was performed concurrently with a secondary task. Nonetheless, the type of the secondary task seems to be a critical factor. Therefore, the data suggest that the mechanisms responsible for the reduction of the interference effect with time are under some attentional control but the exact nature of these mechanisms remains to be explored.