We improve the promising Colour by Correlation method for computational colour constancy by modifying it to work in a three dimensional colour space. The previous version of the algorithm uses only the chromaticity of the input, and thus cannot make use of the information inherent in the pixel brightness which previous work suggests is useful. We develop the algorithm for the Mondrian world (matte surfaces), the Mondrian world with fluorescent surfaces, and the Mondrian world with specularities. We test the new algorithm on synthetic data, and on a data set of 321 carefully calibrated images. We find that on the synthetic data, the new algorithm significantly out-performs all other colour constancy algorithms. In the case of image data, the results are also promising. The new algorithm does significantly better than its chromaticity counter-part, and its performance approaches that of the best algorithms. Since the research into the method is still young, we are hopeful that the performance gap between the real and synthetic case can be narrowed.