The work is well presented, motivated. Applications are interesting and speedups are demonstrated for computing the Slope estimator. The contribution proceeds from a reformulation of the subdifferential of the Slope penalty, and the adaptation of Tibshirani et al. "Strong rule for the Lasso" to this penalty. To improve the general reading, I recommend clarifying the point raised by R#4: "what are the advantages of the subgradients found by this work compared to that of " in the camera ready version.