Our perception of the space around us is not veridical. It has been reported that the systematic errors in our perception of visual space can be described by a reasonably well-behaving space (the resulting space is approximately projective and complies with an affine geometry). The evidence for this is that the perceived centre of a set of points is independent of the order of the steps taken to construct it. We investigated whether this is also the case in displays with well-known 2-D visual illusions. In two examples (Judd and Poggendorff illusions), we show that the perceptual centre of a set of points depends on how this centre is constructed. The misperceptions induced by visual illusions are thus of a different nature than our everyday misperceptions. We argue that the concept of perceived visual space is not very useful for describing human behaviour. We propose an alternative description whereby illusions do not deform a visual space, but only a single visual attribute, leaving other attributes unaffected.