The length of a whole line is overestimated in comparison to the sum of its parts (Künnapas, 1955 Journal of Experimental Psychology 49 134-140). This has been considered to be true for many years, although recent studies have demonstrated that it is not always so. The perception of the length of a whole line is highly dependent on the configuration of its two parts. More precisely, whereas a whole line is perceived as longer than the sum of symmetrically bisected line parts, this overestimation decreases when compared to the sum of the lengths of asymmetrically bisected line parts. Furthermore, the extent of overestimation depends on the degree of asymmetry, so that when the two parts are greatly asymmetric in length, the whole is no longer overestimated (Wolfe et al, 2005 Perception & Psychophysics 67 967-979). Here, two experiments are reported in which a vertical/horizontal line length comparison task was used to investigate how line bisection affects length estimation. The results give rise to a new general principle characterising the mechanisms of visual perception: the sum of the lengths of two asymmetrically bisected parts is perceived as greater than that of two symmetrically bisected parts. Also bisection plays a critical role in length perception by preventing vertical bias.