*PROS: a clean and comprehensive empirical investigation of the influence of different methods of optimizing the quantized representation at test/compression time, and a good ablation study of their proposed method. A good ablation study is provided to justify the effectiveness of each part of the model *CONS: improvements from bitsback coding are relatively marginal Meta-reviewer recommendation: All reviwers voted for acceptance. I recommend the authors to look at the reviewers' comments to improve the paper for the camera ready version.