An alternative to the von Kries scaling underlying the chromatic adaptation transforms found in colour appearance models such as CIECAM02 is suggested for predicting what the colour signal (e.g., XYZ) reflected from a surface under a first illuminant is likely to become when lit instead by a second illuminant. The proposed method, G²M, employs metameric Gaussian-like functions to model the illuminant and reflectance spectra. The method's prediction is based on relighting the Gaussian-like reflectance spectrum with the second Gaussian-like illuminant. Tests show that the proposed G²M method significantly outperforms CIECAT02.