Perceived object colour tends to stay constant under changes in illumination. In the real world, assessing the constancy of object colours typically involves a comparison between the colour we see and the colour we remember; therefore, colour memory must play an important role in the phenomenon of colour constancy.Here we describe two experiments investigating colour memory and colour constancy. Experiment 1 employs 3D domes as stimuli. In this experiment, using an artificial viewing environment with insufficient adaptation, we find a robust dependence of colour constancy on colour memory. This dependence cannot be captured by the most commonly used empirical measure of colour constancy, the Brunswik ratio, which does not incorporate colour memory and does not accurately reflect our findings in this experiment. We therefore develop a new colour constancy index (CCIm) which incorporates colour memory. Calculated in terms of CCIm, the results demonstrate that colour constancy is in fact moderate but imperfect in Experiment 1. Experiment 2 employs 2D natural papers. In this experiment, with longer adaptation time, under real illumination, the obtained CCIm results are all close to 1 (perfect colour constancy), indicating that colour constancy is as good as colour memory allows.