I this paper we present asymmetric matching data that were obtained with a binocular presentation method. Our main motivation was the question whether chromatic adaptation, one of the important mechanisms that contribute to colour constancy, has evolved towards a better performance in the range of colours that are present in the natural image. For the eye adapted to a bluish illuminant for example the presence of an object with a deep yellow colour is very unlikely. So, it was expected that the colour difference between adapting light and target has an influence on the extent of chromatic adaptation. It was found that the colour shift in the observers' matches that can be attributed to chromatic adaptation indeed has a maximum. The location of the maximum, however, was unexpected, i.e. colour differences between target and adapting light that lie around 0.05 u'v'-chromaticity units. Additionally, several models for chromatic adaptation were fitted to our data. It was found that, except for the simple von Kries model, Retinex Theory and difference contrast, a number of models gave good predictions for the L-wave and M-wave fundamental systems, but that predictions for the S-wave system were less accurate.