Andersen and Hardeberg proposed the Hue Plane Preserving Colour Correction (HPPCC) [1], which maps RGBs to XYZs using a set of linear transforms, where each transform is learned and applied in a subregion of colour space, defined by two adjacent hue planes. A hue plane is a geometrical half-plane defined by the neutral axis and a chromatic colour. A problem with the original HPCC method is that the selection of chromatic colors was a user defined choice (and the user might choose poorly) and the method as formed was not open to optimization. In this paper we present a flexible method of hue plane preserving colour correction which we call Hue Plane Preserving Colour Correction using Constrained Least Squares (HPPCC-CLSQ). This colorimetric characterization method is also based on a series of 3 by 3 matrices, each responsible for the transformation of a subregion, defined by two adjacent hue planes, of camera RGB values to the corresponding subregion of estimated colorimetric XYZ values. The matrices are constrained to white point preservation. In this new formulation, the subregions can flexibly be chosen in number and position in order to regularize and optimize the results, whilst constraining continuity crossing the hue planes. The method is compared to a choice of other state-of-the-art characterization methods and the results show that our method consistently gives high colorimetric accuracy for both synthetic and real camera data.