Gamut mapping is a technique to transform out-of-gamut colors to the inside of the output device's gamut. It is essential to develop effective mapping algorithms to realize WYSIWYG (What You See Is What You Get) color reproduction. We had previously found that three-dimensional gamut mapping is superior to the two-dimensional mapping, when we applied Mahalanobis distance as a color difference equation, such as BFD color difference formula, However, in our previous experiments, a clipping method was used that maps all out-of-gamut colors to the surface of the gamut, and no change was made to colors inside the gamut. Since this method could possibly cause loss of gradation in an image, we had investigated non-linear compression for the three-dimensional gamut mapping in this study. The results of visual experiments indicated that preferred compression method depends on image contents. If the saturated colors that are out-of-gamut contain high frequency, a certain degree of compression was needed. On the other hand, if those colors only have gradual change with low frequency, clipping method was more preferred.