As society has become increasingly reliant upon digital images to communicate visual information, a number of forensic techniques have been developed to verify the authenticity of digital images. Amongst the most successful of these are techniques that make use of an image's compression history and its associated compression fingerprints. Little consideration has been given, however, to anti-forensic techniques capable of fooling forensic algorithms. In this paper, we present a set of anti-forensic techniques designed to remove forensically significant indicators of compression from an image. We do this by first developing a generalized framework for the design of anti-forensic techniques to remove compression fingerprints from an image's transform coefficients. This framework operates by estimating the distribution of an image's transform coefficients before compression, then adding anti-forensic dither to the transform coefficients of a compressed image so that their distribution matches the estimated one. We then use this framework to develop anti-forensic techniques specifically targeted at erasing compression fingerprints left by both JPEG and wavelet-based coders. Additionally, we propose a technique to remove statistical traces of the blocking artifacts left by image compression algorithms that divide an image into segments during processing. Through a series of experiments, we demonstrate that our anti-forensic techniques are capable of removing forensically detectable traces of image compression without significantly impacting an image's visual quality. Furthermore, we show how these techniques can be used to render several forms of image tampering such as double JPEG compression, cut-and-paste image forgery, and image origin falsification undetectable through compression-history-based forensic means.