Drifting lines that are not orthogonal to their direction of motion appear to travel more slowly than those that are, resulting in a ‘speed reduction’ illusion. It has been shown that several factors affect the strength of this illusion such as the angle of tilt, the stimulus contrast and the line length [Castet, Lorenceau, Shiffrar, & Bonnet, Vision Research 33 (1993) 1921–1936]. We show here that the illusion is also affected strongly by other factors, notably the spatial arrangement of multi-element displays and whether there is a random component to the image motion. An array of short lines that are co-linear is processed in a manner similar to a continuous long line, whereas the same array distributed randomly in space is treated by the visual system as a group of independent short lines. Random variation of the length or position of a line as it is drifting abolishes the speed reduction illusion completely. The data indicate that even for simple stimuli, vector summation of local motion components with velocity signals arising at the line ends cannot, on its own, account for perceived speed.