The line-bisection task is the standard assessment of unilateral visual neglect. It supplies one effect, the crossover effect, that challenges models of neglect: in left neglect, the rightward displacement of the midpoint of the line becomes a left displacement for small lines. We review the various attempts to account for the cross-over effect, before describing a computational model of performance in the line-bisection task that produces a cross-over effect quite naturally in its damaged state. The model trades on aspects of several current theories of neglect, including independent attentional processing in the two hemispheres, each of which possesses an attentional gradient in which the contralateral field is accentuated. We assume a small residual noise, along the same gradient, in the damaged hemisphere. When lesioned to simulate right hemisphere damage, the model produces line bisections similar to human performance, in terms of the relationship with line length, a variable cross-over point for the smaller lines, and an amelioration of performance with leftside, but not rightside cueing.