A method of outlier detection is proposed as a way of improving illumination-estimation performance in general, and for scenes with multiple sources of illumination in particular. Based on random sample consensus (RANSAC), the proposed method (i) makes estimates of the illumination chromaticity from multiple, randomly sampled sub-images of the input image; (ii) fits a model to the estimates; (iii) makes further estimates, which are classified as useful or not on the basis of the initial model; (iv) and produces a final estimate based on the ones classified as being useful. Tests on the Gehler colorchecker set of 568 images demonstrate that the proposed method works well, improves upon the performance of the base algorithm it uses for obtaining the sub-image estimates, and can roughly identify the image areas corresponding to different scene illuminants.