The addition of white noise to an image has been shown to increase the perceived sharpness of the image's blurred regions under certain conditions. Additive white noise has also been shown to increase the visual quality a compressed image, a finding which has been attributed, in large part, to the noise's ability to simulate textures that have been lost via the compression. To explore the perceptual underpinnings of this enhancing effect, in this paper, we tested whether the noise can be tuned based on properties of the source texture to provide even greater improvements in quality as compared to white noise. We used a parametric texture-synthesis algorithm to generate statistically and spectrally shaped noise patterns, which were scaled in contrast and then added to corresponding compressed texture regions. Subjects reported both the optimal contrast scaling factors and the associated quality improvement scores relative to the distorted regions. Our results indicate that the addition of the shaped noise can provide markedly greater quality improvements compared to white noise, a finding which cannot be explained by the mere presence of high-frequency content. We discuss how the optimal contrast scalings might be predicted, and we examine the performances of existing quality assessment algorithms on our enhanced images.