In order to systematically evaluate different gamut mapping algorithms, we have simulated gamut mapping on a CRT using simple rendered images of colored spheres floating in front of a gray background. Using CIELab as our device-independent color space, cut-off values for lightness and chroma, based on the statistics of the images, were chosen to reduce the gamuts for the test images. The gamut mapping algorithms consisted of combination of clipping and linearly mapping the original gamut in piecewise segments. Complete color space compression in RGB and CIELAB was also used. Each of the colored originals (R,G,B,C,M,Y, and Skin) were mapped separately in lightness and chroma. In addition, each algorithm was implemented with saturation (C*/L*) allowed to vary or remain constant. Using a paired-comparison paradigm, pairs of test images with reduced color gamuts were presented to twenty subjects along with the original image. For each pair the subjects chose the test images that better reproduced the original. Rank orders and interval scales of algorithm performance with confidence limits were then derived. Certain algorithms were found to perform best consistently over image color. For chroma mapping, clipping of all out-of-gamut colors while keeping lightness constant was the most preferred method. For lightness mapping at the top of the gamut, a particular piecewise mapping technique while keeping saturation constant was preferred. For lightness mapping at the bottom the results gave an indication of the type of algorithm that might be best while keeping chroma constant. The choice of device-independent color space may also influence the choice of gamut mapping algorithm.