In his paper we introduce two improvements to the three-dimensional gamut mapping approach to computational colour constancy. This approach consist of two separate parts. First the possible solutions are constrained. This part is dependent on the diagonal model of illumination change, which in turn, is a function of the camera sensors. In this work we propose a robust method for relaxing this reliance on the diagonal model. The second part of the gamut mapping paradigm is to choose a solution from the feasible set. Currently there are two general approaches for doing so. We propose a hybrid method which embodies the benefits of both, and generally performs better than either. We provide results using both generated data and a carefully calibrated set of 321 images. In the case of the modification for diagonal model failure, we provide synthetic results using two cameras with a distinctly different degree of support for the diagonal model. Here we verify that the new method does indeed reduce error due to the diagonal model. We also verify that the new method for choosing the solution offers significant improvement, both in the case of synthetic data and with real images.