This article describes an investigation of several chroma compression algorithms with constant and modified lightness and hue. While the rescaling of differing lightness ranges is not considered here, gamut-mapping algorithms with different mapping types and mapping directions are evaluated. Among these are the methods of mapping colors towards a focal point as well as the newly developed relative lightness change (RLC) technique. The latter maps colors along curved lines and enables the direct use of cylindrical coordinates lightness, chroma, and hue for the mapping, regardless of the mapping direction. Moreover, the RLC method is straightforward and does not need any iteration or complex cross sectioning, thus it is well suited for real time gamut mapping. Issues of gamut mapping such as the mapping space, the coordinate system within the space, and gamut boundary description are discussed. Psychophysical experiments are described which were conducted to evaluate the reproduction of monitor images on a device with a clearly smaller color gamut. All images were viewed on the monitor. The algorithms were dependent on the image gamuts. The experiments showed that the RLC method performs superior compared to the focal mapping algorithms. Moreover, the optimum mapping direction was RLC50 that means a slight adaptation of lightness. The best mapping type was pure clipping, regardless of the mapping direction. Notably, RLC50 outperformed other, recently published algorithms. While the found algorithms may still require some fine-tuning, a thorough understanding of the mechanisms of gamut mapping was acquired.