We present a perceptual model for hiding a spread-spectrum watermark of variable amplitude and density in an image. The model takes into account the sensitivity and masking behavior of the human visual system by means of a local isotropic contrast measure and a masking model. We compare the insertion of this watermark in luminance images and in the blue channel of color images. We also evaluate the robustness of such a watermark with respect to its embedding density. Our results show that this approach facilitates the insertion of a more robust watermark while preserving the visual quality of the original. Furthermore, we demonstrate that the maximum watermark density generally does not provide the best detection performance.