Recently, Convolutional Neural Networks (CNNs) have been widely used to solve the illuminant estimation problem and have often led to state-of-the-art results. Standard approaches operate directly on the input image. In this paper, we argue that this problem can be decomposed into three channel-wise independent and symmetric sub-problems and propose a novel CNN-based illumination estimation approach based on this decomposition. The proposed method substantially reduces the number of parameters needed to solve the task while achieving competitive experimental results compared to state-of-the-art methods. Furthermore, the practical application of illumination estimation techniques typically requires identifying the extreme error cases. This can be achieved using an uncertainty estimation technique. In this work, we propose a novel color constancy uncertainty estimation approach that augments the trained model with an auxiliary branch which learns to predict the error based on the feature representation. Intuitively, the model learns which feature combinations are robust and are thus likely to yield low errors and which combinations result in erroneous estimates. We test this approach on the proposed method and show that it can indeed be used to avoid several extreme error cases and, thus, improves the practicality of the proposed technique.