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The efficient compression of color images requires a step that takes the dependencies between the color components into account. This is mostly realized with a color transformation, mapping the red, green, and blue components into another representation. The transformation must be reversible if the compression system is to support the lossless reconstruction of the images. In this paper, we propose an entire family of multiplierless reversible color transforms and investigate their performance in lossless image compression. When using the LOCO-I algorithm or lossless JPEG2000 for compression, results show that the compression performance (in terms of bits per pixel) using the optimal color-space selection leads to a distinct reduction of the mean bitrate, compared to any fixed color space. Furthermore, it is shown that it is possible to automatically select a suitable color space without significant loss in compression efficiency, compared to the optimal selection. This automatic selection improves the compression performance independently of whether LOCO-I or JPEG2000 is applied.