Gamut boundary determination is an important step in device characterisation and colour gamut mapping. Many different algorithms for the determination of colour gamuts are proposed in the literature. They vary in accuracy, computational efficiency, and complexity of the resulting triangulated gamut surface. Recently, an algorithm called uniform segment visualization (USV) was developed. The gamut surfaces produced by the USV algorithm is more accurate than the ones produced by the the segment maxima algorithm, while at the same time, they are significantly simpler than the ones produced by the somewhat more accurate modified convex hull. In this paper, we propose a new method. First, an accurate gamut boundary is computed using the modified convex hull. The resulting surface is then simplified using an established mesh decimation technique. This results in surfaces that are significantly more accurate than the ones produced by the USV algorithm at a comparable complexity.