We derive capacity bounds for watermarking and data hiding in the presence of JND perceptual coding for a class of techniques that do not suffer from host signal interference. By modeling the lossy compression distortions on the hidden data using non-Gaussian statistics, we demonstrate that binary antipodal channel codes achieve capacity. It is shown that the data hiding capacity is at most equal to the loss in storage efficiency bit rate if watermarking and quantization for lossy compression occur in the same domain.