The human parietal cortex exhibits a preference to contralaterally presented visual stimuli (i.e., laterality) as well as an asymmetry between the two hemispheres with the left parietal cortex showing greater laterality than the right. Using visual short-term memory and perceptual tasks and varying target location predictability, this study examined whether hemispheric laterality and asymmetry are fixed characteristics of the human parietal cortex or whether they are dynamic and modulated by the deployment of top-down attention to the target present hemifield. Two parietal regions were examined here that have previously been shown to be involved in visual object individuation and identification and are located in the inferior and superior intraparietal sulcus (IPS), respectively. Across three experiments, significant laterality was found in both parietal regions regardless of attentional modulation with laterality being greater in the inferior than superior IPS, consistent with their roles in object individuation and identification, respectively. Although the deployment of top-down attention had no effect on the superior IPS, it significantly increased laterality in the inferior IPS. The deployment of top-down spatial attention can thus amplify the strength of laterality in the inferior IPS. Hemispheric asymmetry, on the other hand, was absent in both brain regions and only emerged in the inferior but not the superior IPS with the deployment of top-down attention. Interestingly, the strength of hemispheric asymmetry significantly correlated with the strength of laterality in the inferior IPS. Hemispheric asymmetry thus seems to only emerge when there is a sufficient amount of laterality present in a brain region.