Thank you for the very detailed responses to the comments from the two reviewers. Particularly through your more detailed treatment of the IPD it seems that you should be able to make a new version that will satisfy most of the concerns of the reviewers. I am therefore now happy to encourage you to prepare the new version, which I expect to send back for re-review.

Of course the reviewers are the experts, and I only want to add comments on two issues that I feel you have not fully explained in your responses.

1. On the analytical isde, I still don't feel that I understand how you can end up at a precision of 1 ppb when you have blanks varying by 10 ppb. Nor do I really understand how you arrive at a headline figure of 1 ppb when the mean absolute difference between replicate measurements was about 2 ppb. I think this might require more thought as my feeling is that the reviewers will share my concerns.

2. For the IPD, I do appreciate the multiple parallel calculations, but again have two concerns. The first is simply presentational. In Fig R2 the Siple based reconstruction, central to your paper is almost completely invisible. But now I look at it in Fig R3 and it is completely different from what you showed in the original paper (Fig 3). The absolute values of IPD (NEEM/SD) there ranged from ~42-52 ppb, now you show 30-48. The shape is different as well. This is not a question that WAISDivide differs from SD, but your SD/NEEM profile has changed considerably, and yet I can't find any discussion of this in the response. The IPD at 11.5 ka, using the same (NEEM/SD) data, has changed from 52 to around 35 ppb, a very considerable change. Have you resynchronised or changed some values? Please address this in the material you submit with the paper that addresses the review comments.

Some smaller points from me:
You say Fig R1 includes Fluckiger but i don't see it.
For the second rev, Fig R1, you should use the same y-scale for panels a and b so readers can compare the magnitude of variations directly.

Thank you for the considerable changes you have made to the paper. These have certainly improved it. I apologise for the delay in obtaining reviews on this version. As you will see, I sent the new version to two reviewers - one was the same as for the previous version, the other was a new reviewer. Both reviewers agree that your paper is valuable and should eventually be published. However, although they go into different levels of detail, both still have significant issues on two aspects of your paper: the analytical uncertainty you quote, and the use of SD data for the IPD. You need to address their detailed comments as well as these two major issues.

I would like to particularly emphasise the need to either alter or explain better the uncertainty calculation. Your paper has been seen by 3 reviewers, all of them VERY familiar with measurements of methane in ice and with the sources of error in such measurements. Despite your explanations all 3 of them (and me as editor) still don't understand how it is possible, when you have a strongly varying blank, to arrive at such a small uncertainty. As one reviewer says, you need either to come up with a convincing discussion of this, or resist the temptation to claim a very low uncertainty.

I would also like to expand further rev 1's comment about the blank. They correctly point out that, if you draw 4 samples from the range 5-15 ppb, the SE of the mean (SD/2) is indeed around 2 ppb. This implies that the intraday uncertainty is no less than the inter-day uncertainty. The uncertainty on each sample is controlled by the blank of that sample, not by the uncertainty of the daily average so you should not be dividing by root(4) to obtain it. It seems impossible that the uncertainty on a measurement can actually be less than the standard deviation of the blank measurements, which presumably is 4 ppb.

I look forward to seeing a revised manuscript.

Thank you again for your constructive response to the reviewers. Although I think your method of calculating the uncertainty remains open to question, I think (based also on the data in Table 1) the value you are using is probably reasonable, and that there is no value in pursuing this further. I am therefore not sending the paper back for further review but instead accepting it subject to minor changes.

I have a couple of points about the English (copy editors may have more):
Page 3, line 27, remove "Since" so that the snetence makes sense
Line 36, replace "Despite" with "Although"

Page 10, line 39. This should surely read "Fig 7" not "Fig 6"

You have moved much material from SI into main text but you left duplicate figures in SI. This is not needed, please remove them: Fig S1 is Fig 3; Fig S2 is Fig 5; the material in Fig S3 is in Fig 8; and Fig S4 is Fig 4.

Table 1: It would be useful to add a column showing the difference between the mean of the 1st measurement and the mean of the 2nd measurement, as this is the statistic that indicates that your error estimate might be OK.