Abstract Lossy compression algorithms aim to compactly encode images in a way which enables to restore them with minimal error. We show that a key limitation of existing algorithms is that they rely on error measures that are extremely sensitive to geometric deformations (e.g. SSD, SSIM). These force the encoder to invest many bits in describing the exact geometry of every fine detail in the image, which is obviously wasteful, because the human visual system is indifferent to small local translations. Motivated by this observation, we propose a deformation-insensitive error measure that can be easily incorporated into any existing compression scheme. As we show, optimal compression under our criterion involves slightly deforming the input image such that it becomes more “compressible”. Surprisingly, while these small deformations are barely noticeable, they enable the CODEC to preserve details that are otherwise completely lost. Our technique uses the CODEC as a “black box”, thus allowing simple integration with arbitrary compression methods. Extensive experiments, including user studies, confirm that our approach significantly improves the visual quality of many CODECs. These include JPEG, JPEG 2000, WebP, BPG, and a recent deep-net method