The dimensional overlap (DO) model proposes distinct mechanisms for stimulus-stimulus (S-S) and stimulus-response (S-R) conflict effects. Many studies have examined the independence of S-S and S-R conflict effects in the color-word Stroop and Simon tasks. However, confounds exist between the distinction of DO (i.e., S-S dimensional overlap compared with S-R dimensional overlap) and the distinction of stimulus attributes (e.g., color compared with spatial location; semantic compared with nonsemantic information), which may hinder interpretation of the independence of S-S and S-R conflicts. A spatial Stroop (word) task and a spatial Stroop (arrow) task were combined with a Simon task in Experiments 1 and 2, respectively to eliminate these confounds of stimulus attributes. The results showed that S-S and S-R conflicts affected performance additively. There was no significant correlation across participants. These findings lend further support to independent processing of S-S and S-R conflicts as it is outlined in the taxonomy of DO.