The authors' have responded adequately to many of my comments from the previous review.  I have the following additional comments for the authors' consideration.

1. On the top of page 5, the authors write that analysts can take the DP mechanism into account in inferences.  This is true for data independent DP mechanism, which is a strong argument in favor of them, but it is not true of all DP mechanisms, e.g., data dependent ones.  I suggest that this statement be given appropriate caveats, e.g., adding the clarification "for many types of DP algorithms" or "for data independent DP algorithms like those examined here".


2. On page 13, I suggest adding a sentence indicating the epsilon and delta used in OnTheMap, which is the most prominent (only?) differentially private data release of a statistical agency.  The values are in the paper.  This would give readers a sense as to what has been used in practice, which are values greatly exceeding those recommended in the formal privacy literature.  Also, on this page, I think it is worth stressing that selection of epsilon (or delta) is a policy decision, not a statistical decision.  Further, it is one that policy makers are not experienced considering in practical contexts, which points to the need for additional research.

3.  On page 31, I suggest that the authors note the challenges of adopting their recommended strategy -- perturb interior cells -- in high dimensions.  Many surveys collect data on dozens or hundreds of variables, with only tens of thousands of sampled cases.  It may be impossible even to get the full table to fit in computer memory.  The implied tables also are massively sparse, with many sampling zeros.  These features can render useless the strategy of adding independent noise to each cell, at least in the non-interactive setting, for high dimensional data products.  This again points to an area for research.