Uniform quantization of wavelet coefficients introduces perceptually disturbing artifacts by decreasing the visual smoothness. In this paper, the local Holder regularity is used to quantify these changes in visual smoothness. A modified uniform quantization scheme that constrains local regularity reduction is proposed. The quantizer modification is applicable to any uniform quantization scheme and requires no additional side information to be transmitted to the decoder, unlike standard deadzone quantizers. The reconstructed images show a noticeable perceptual improvement as well as an increased PSNR relative to uniform quantization.