When marking the subjective midpoint of a horizontal line, patients with left unilateral neglect typically deviate rightward. Different accounts of this pattern of performance refer either to a biased competition between the two hemi-segments of the line, with the right part being subjectively perceived as longer than the left part, or to a distortion of a cognitive representation of space, with spatial coordinates progressively relaxing from the right to the left. These accounts make different predictions about the role of the right part of the line, which is crucial in the biased competition account, but less important in the distortion account. To test these predictions, we asked participants to set the endpoints and the centre of perceived and imaginary lines. Contrary to previous studies, we controlled for the direction of performance of the endpoint task, with left-to-right trials and right-to-left trials being performed in separate blocks. Five patients with right-hemisphere lesions and left neglect demonstrated the typical asymmetries when a right-sided stimulus (segment or endpoint) was present, but showed either normal performance or a reversed (leftward) bias while setting the endpoints and the centre of an imaginary line starting from the left side, when no right-sided visual stimulus was present until completion of each trial. We concluded that the right-sided portion of the line has a crucial importance in determining patients' rightward deviations in line bisection, consistent with the biased competition hypothesis and with neurocognitive models of attentional orienting.