Automatic white balancing works quite well on average, but seriously fails some of the time. These failures lead to completely unacceptable images. Can the number, or severity, of these failures be reduced, perhaps at the expense of slightly poorer white balancing on average, with the overall goal being to increase the overall acceptability of a collection of images? Since the main source of error in automatic white balancing arises from misidentifying the overall scene illuminant, a new illuminationestimation algorithm is presented that minimizes the high percentile error of its estimates. The algorithm combines illumination estimates from standard existing algorithms and chromaticity gamut characteristics of the image as features in a feature space. Illuminant chromaticities are quantized into chromaticity bins. Given a test image of a real scene, its feature vector is computed, and for each chromaticity bin, the probability of the illuminant chromaticity falling into a chromaticity bin given the feature vector is estimated. The probability estimation is based on Loftsgaarden-Quesenberry multivariate density function estimation over the feature vectors derived from a set of synthetic training images. Once the probability distribution estimate for a given chromaticity channel is known, the smallest interval that is likely to contain the right answer with a desired probability (i.e., the smallest chromaticity interval whose sum of probabilities is greater or equal to the desired probability) is chosen. The point in the middle of that interval is then reported as the chromaticity of the illuminant. Testing on a dataset of real images shows that the error at the 90^th and 98^th percentile ranges can be reduced by roughly half, with minimal impact on the mean error.