The design of a gamut mapping algorithm (GMA) is always a compromise between preserving different competing aspects such as color, contrast, and lightness. A natural requirement of a GMA is that the algorithmic treatment of this competition has to avoid any additional artifacts such as discontinuities or loss of contrast. In this work, several common gamut mapping algorithms are studied from this aspect, resulting in the observation that problems with geometric discontinuities are widespread. For the assessment of the phenomena induced by local mapping properties, an algorithmic test is developed and applied. This new test supports both the quality check of existing as well as the development of new GMAs.