A wavelet-based perceptual image coder for the compression of color images is proposed here in which the coding structure is coupled with Human Visual System models to produce high quality images. The major contribution is the development of a new model for the compression of the color components based on psychovisual experiments, which quantifies the optimum amount of compression that can be applied to the color components for a given rate. The model is developed for YCbCr color space and the perceptually uniform CIE Lab color space. A complete coding structure for the compression of color images is developed by incorporating the new perceptual model. The performance of the proposed coder is compared with a wavelet-based coder that uses the quantization stage of the JPEG2000 standard. The perceptual quality of the compressed images is tested using the wavelet-based subjective and objective perceptual quality matrices such as Mean Opinion Score, Visual Information Fidelity and Visual Signal to Noise Ratio. Though the model is developed for a perceptually lossless high quality image compression, results obtained reveal that the proposed structure gives very good perceptual quality compared to the existing schemes for lower bit rates. These advantages make the proposed coder a candidate for replacing the encoder stage of the current image compression standards.