In two experiments we investigated whether the dynamics of standing upright were lateralized. The postural task of Experiment 1 introduced a lateral bias of attention; the postural task of Experiment 2 did not. In Experiment 1, six left-handed and six right-handed participants passively held a laser pointer at the side of the body in either the left or right hand. Successful pointing at targets that varied in distance and size required minimizing the body's medio-lateral (ML) sway. Sway variability, in the range of 2.8–5 mm, was smaller in the anterior–posterior (AP) direction (of relevance to keeping upright) and larger in the ML direction when the pointer was on the preferred rather than non-preferred side. In Experiment 2, six left-handed and six right-handed participants maintained quiet stance while visually fixating a target. Variability of ML and AP sway changed in the same way with difficulty of the precision aiming task and did so independently of handedness. Discussion focused upon the possible mechanism of postural lateralization and the nature of the tasks by which such lateralization is revealed.