There are many works in colour that assume illumination change can be modelled by multiplying sensor responses by individual scaling factors. The early research in this area are sometimes grouped under the heading von Kries adaptation: the scaling factors are applied to the cone responses. In more recent studies, both in psychophysics and in computational analysis, it has been proposed that scaling factors should be applied to linear combinations of the cones which have narrower support: they should be applied to the so-called “Sharp Sensors”. In this paper we generalise the computational approach to spectral sharpening in three important ways. First, we introduce Spherical Sampling as a tool that allows us to enumerate in a principled way all linear combinations of the cones. This allows us to, second, find the optimal sharp sensors which minimises a variety of error measures including CIE Delta E (previous work on spectral sharpening minimised RMS) and colour ratio stability. Lastly, we extend the spherical sampling paradigm to the multispectral case. Here the objective is to model the interaction of light and surface in terms of colour signal spectra. Spherical sampling is shown to improve on the state of the art.