Although asymmetric colour matching has been widely used in experiments on colour constancy, an exact colour match between objects lit by different chromatic lights is impossible to achieve. We used a modification of this technique, instructing our observers to establish the least dissimilar pair of differently illuminated coloured papers. The stimulus display consisted of two identical sets of 22 Munsell papers illuminated independently by neutral, yellow, blue, green and red lights. The lights produced approximately the same illuminance. Four trichromatic observers participated in the experiment. The proportion of exact matches was evaluated. When both sets of papers were lit by the same light, the exact match rate was 0.92, 0.93, 0.84, 0.78 and 0.76 for the neutral, yellow, blue, green and red lights, respectively. When one illumination was neutral and the other chromatic, the exact match rate was 0.80, 0.40, 0.56 and 0.32 for the yellow, blue, green and red lights, respectively. When both lights were chromatic, the exact match rate was found to be even poorer (0.30 on average). Yet, least dissimilar matching was found to be rather systematic. Particularly, a statistical test showed it was symmetric and transitive. The exact match rate was found to be different for different papers, varying from 0.99 (black paper) to 0.12 (purple paper). Such a variation can hardly be expected if observers' judgements were based on an illuminant estimate. We argue that colour constancy cannot be achieved for all the reflecting objects because of mismatching of metamers. We conjecture that the visual system might have evolved to have colour constant perception for some ecologically valid objects at a cost of colour inconstancy for other types of objects.