The CIE94 colour difference equations are known to give good predictions of subjective colour differences for viewing under reference conditions. We have psychophysically, tested whether the equations also give useful predictions when the conditions are relaxed. In particular, we collected subjective colour difference data with (i) chromatic illuminants, (ii) textured samples, and (iii) large colour differences. The predicted differences, to be compared with the measured subjective differences, were calculated by using von Kries transform to predict colour appearance under D65, followed by application of the CIE94 equations (with the default lightness, chroma, and hue weightings). We found that subjective colour differences were not predicted properly. However, if texture i accounted, for by modifying predicted colour differences by a sample-pair dependent linear function, then prediction is successful for all data points apart from those corresponding to illumination under a strongly saturated red illuminant. The fit of this model and its utility in predicting illuminants that enhance colour differences was confirmed by statistical tests.