This paper makes an important contribution to the practice of large-scale Gaussian process inference. Many of the reviewers' concerns were addressed in the rebuttal. However, for the camera-ready version of the paper, I strongly encourage the authors to (1) clarify and include additional implementation details, (2) make clear how their approach differs from past work (if it does differ), and (3) include the promised new experiments with ARD priors and more train/test splits. These changes with help to maximize the paper's impact. Furthermore, please clarify the "more powerful preconditioning" language in the abstract, as suggested by Reviewer 3.