We propose a new approach to the problem of optimizing autoencoders for lossy image compression. New media formats, changing hardware technology, as well as diverse requirements and content types create a need for compression algo- rithms which are more flexible than existing codecs. Autoencoders have the po- tential to address this need, but are difficult to optimize directly due to the inherent non-differentiabilty of the compression loss. We here show that minimal changes to the loss are sufficient to train deep autoencoders competitive with JPEG 2000 and outperforming recently proposed approaches based on RNNs. Our network is furthermore computationally efficient thanks to a sub-pixel architecture, which makes it suitable for high-resolution images. This is in contrast to previous work on autoencoders for compression using coarser approximations, shallower archi- tectures, computationally expensive methods, or focusing on small image.