Even though there is still room for improvement, recent perceptual image-difference measures show a prediction performance that makes them interesting to be used as objective functions for optimizing image processing algorithms. In this paper, we use a color enhanced modification of the Structural Similarity (SSIM) index for optimizing gamut mapping. An iterative algorithm is proposed that minimizes this measure for a given reference image subject to in-gamut images. Since distortions within remote image regions contribute independently to the measure a descent direction can be specified locally. The step-length is chosen to be a fraction of the just-noticeable-distance ensuring a decrease of the measure. Results show that the proposed approach preserves contrast and structural information of reference images. Some artifacts suggest modifications of the employed image-difference measure.