Many studies have argued for distinct but complementary contributions from each hemisphere in the control of movements to visual targets. Investigators have attempted to extend observations from patients with unilateral left- and right-hemisphere damage, to those using neurologically-intact participants, by assuming that each hand has privileged access to the contralateral hemisphere. Previous attempts to illustrate right hemispheric contributions to the control of aiming have focussed on increasing the spatial demands of an aiming task, to attenuate the typical right hand advantages, to try to enhance a left hand reaction time advantage in right-handed participants. These early attempts have not been successful. The present study circumnavigates some of the theoretical and methodological difficulties of some of the earlier experiments, by using three different tasks linked directly to specialized functions of the right hemisphere: bisecting, the gap effect, and visuospatial localization. None of these tasks were effective in reducing the magnitude of left hand reaction time advantages in right handers. Results are discussed in terms of alternatives to right hemispheric functional explanations of the effect, the one-dimensional nature of our target arrays, power and precision given the size of the left hand RT effect, and the utility of examining the proportions of participants who show these effects, rather than exclusive reliance on measures of central tendency and their associated null hypothesis significance tests