Response inhibition is a main function of cognitive control and its neural substrates have been studied extensively. However, it is still a question whether previous brain imaging investigations were successful in isolating specific response inhibition activation. In the current study we attempted to pinpoint response inhibition in the brain using a Go/No-go task and fMRI, by contrasting rare-No-go trials with prevalent-No-go trials. Although inhibition is required in all No-go trials, task variants with rare-No-go cases (25%) create a prepotent response which elicits a strong demand for inhibition, while task variants with prevalent-No-go cases (75%) require very little inhibition effort. Since the neural activation in this design is extracted solely from No-go trials, differing only in the extent of inhibitory demand, the analysis avoids contamination of the data with motor effects or visual factors. Using this experimental design we highlight the contribution of the parietal cortex (bilaterally) to inhibitory processes, while casting doubts about the specificity of frontal activation in such processes. Future studies are required to verify that bilateral intraparietal sulcus and left temporo-parietal junction activations could be markers of inhibitory control.