Comments from Peter Bussey Line 28 First sentence is a little cumbersome - I suggest to insert "recorded" before "at" and add a comma after HERA. Perhaps better: Data from....,ep, have been central.....[1]. Such data have been recorded at....at HERA. Then run on to continue with contents of second paragraph. 33 These analyses were based.... [avoid repetition] 34 I think you should not assume familiarity but state the order that these fits were performed so that the readers know exactly where things stood before this analysis. 36 Define NNLO .... inclusive DIS data [2] 37 Omit sentence, no need to make excuses. 38 The present analysis has been made possible by the recent provision of jet cross section predictions for ep scattering at NNLO by the NNLOJET authors and their collaborators. [be positive!] 41 to be constructed from -> to originate from 42 Can you say something more precise than "treated"? 46 omit "both" 49 All -> The [repetition with "entirely"] I think I would again say "inclusive DIS" 50 Omit "highly" - it's consistent or it is not. The sentence really needs a phrase of amplification - why should it not be consistent? Why is it a single data set and not two? 51 Omit "very" 53 Reference for this statement. I would omit sentence "It is..." and rephrase a bit. "With the assumption that it is also valid in hadron-hadron physics, PDF fits can be made to LHC data. However, they can be biased by any presence of physics beyond the Standard Model (BSM), including this tacitly in the fitted PDF values and thereby reducing the sensitivity to explicit searches for BSM physics owing to biased background predictions." 58 Omit final sentence, not needed. 62 coherent? Above it was "consistent". I'd stick with that but say what it means. 67 ... squared in the DIS process, This sentence has "published" three times! Omit "which were...[27]" as it is just background information here and makes the sentence cumbersome. 71 Omit ", however, only" [Basically, the reader just needs the facts.] Since the reader may now be a little confused as to what "new" means, I would repeat the reference or else mention the present analysis. 73 Say:... were excluded in order to ensure convergence of the perturbative series [EXPLAIN THIS!] and to ensure that the NNLO scale uncertainties were no greater tha 10%..... I think the rest of the text here is too chatty and you need to stick to the basic points. 76 $b$ 78 "bin" is jargon, should we say "interval" ? [passim] 78-9,82 had to be excluded -> were excluded [passim, too chatty] 80 were judged to be -> were [avoid subjectivity] 89 The present analysis was performed in the same way as the previous [more concise] 90 Does this mean "cros-section data with Q^2 > 3.5 GeV^2"? If so, say it like that; if not, make the meaning clearer? 91 I think you should repeat the crucial chisq definition here. 92 State what you mean by evolution and mention DGLAP (again). 97 Can you reference the second program?? 100 As explained in the next section? Better say that. 103 ... was made possible by the.... [sounds more forceful!]. Repeat the reference. 116 results 119 Could just say "For the gluon PDF, an additional term..." 123 I think this sentence would be better at the start of the section. 132-137 I think these lines should go before the sentence starting line 125. However it becomes a little unclear at what point the addition of new parameters stopped. If this means when all the parameters in 132-137 were used, and this was optimal, then I'd say "... could not be improved by inclusion of further terms". (which are not included in 132-137, I suppose.) 139 equal, Bubar=Bdbar, resulting in a single... 153 How did you assign the variations that were used? 177 etc fixed points? 182 Clarify or omit sentence. 204 Omit "It was checked that" 211 is differentd -> differs 215 Somehow this paragraph seems to be left hanging. 224 ... uncertainties", which.... 226 This source of uncertainty [suddenly "uncertainty" become singular.] 234 omit "so-called" but remind reader what this chisq means. 240 ... uncertainty, which dominates the uncertainties. 241 Eq. 7 doesn't seem to be there. 245 Omit the vague word "significantly" ? 249-252 Consider moving this paragraph up a bit, near to where the chisq is first discussed in this section. 256 Well there can be no doubt about the minima! I would simply say that the positions of minimum chisquared are in close agreement, indicating that any anomalies at low Q^2 are small. 258 This is hardly surprising since inclusive DIS is dominated by a QED vertex. It would be as well to remind the reader of this, perhaps at the start of the section where you correctly say that jets are essential. Does fig 2c add anything to the paper? 271 analyses 277 which is similar to the cut used here. 278 ... that both the H1 and...were performed 286 Consider just calling it "NNLO PDF evaluation" 297 I'd rearrange: it becomes questionable to quantify the theory uncertainties.... 302 Not sure what "map out" means. 333 entered -> used 337, 358 Omit very 340 For completeness add "DIS" into the sentence. 342 ... have been used... 343 called -> denoted as 345 Maybe: ... with alphaS allowed to vary freely.. 347 This result for... 350 for -> with Fig 7, 8. You might consider replacing the green by light blue to assist the colour-blind. (I add that this does not include me) However if you had no complaints before, perhaps this is not so important. Comment: A first reaction is why not include the PDF set with floating alphaS and uncertainties associated with this method. I can understand a rationale: a future user might want to use yet another value of alphaS, perhaps with an uncertainty, and hopefully will be able to extract the desired information from the two sets you have provided. It might be good to make this explicit.