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I have been asked by a top journal in my field (mathematics) to referee a paper. The paper is very strong, but I feel that it falls slightly short of making the cut for this (very prestigious) journal. In fact I believe I would recommend acceptance of the paper if it was submitted to virtually any less prestigious journal. How would I go about communicating this sentiment in the report?

For example, I have thought about explicitly recommending some journals for the author to submit to.

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    I would say so directly in the report. I have done this in my reports and also had such reports of my own papers.
    – Moishe Kohan
    Oct 27 at 22:14
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    Can you be m9re explicit about why you feel the paper doesn't make the cut? Is the research not impactful enough?
    – Scott Seidman
    Oct 28 at 20:49
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    @ScottSeidman Does it matter? Probably answering that question would get too field-relevant for this question that is otherwise fine. This site has a habit of getting into too much inappropriate detail in math/CS since that represents if not the majority, the plurality of the uesrbase.
    – Azor Ahai -him-
    Oct 28 at 20:55
  • @AzorAhai-him- I would say that If you're going to suggest a strong paper is not right for a high profile journal, and you're wondering how to tell the author and/or editor this, saying why is a step in the right direction.
    – Scott Seidman
    Oct 29 at 15:39
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    @ScottSeidman Sure, anonymousx should tell the authors and editors why, but I thought you were asking them be more explicit to us.
    – Azor Ahai -him-
    Oct 29 at 15:40

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I suggest that you can say that to the editor, but not to the author. Alternatively, ask the editor whether they would object. Saying that the paper is nice but not sufficiently novel or whatever for this journal is fine (IMO), but less fine is naming other journals.

The author, if rejected, probably knows already that other journals exist and may have a plan without your prompting. Some authors just take a shot at the top, hoping for the best.

But your relationship with the editor and the publisher is also important.

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    Why not recommending other journals? I was thankful for such recommendations when my paper was rejected because it did not fit the scope of the journal I submitted to. Back then, I was not aware of all the recommended journals.
    – usr1234567
    Oct 28 at 23:22
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    -1: recommending other journals in a referee report is fairly common, and I'm not aware of an editor having issues with it.
    – Martin Argerami
    Oct 29 at 2:00
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    Can you elaborate a bit what you mean exactly? I really do not see how recommending other journals could cause issues with the editor or the publisher, especially in the field in question (math).
    – testaccount
    Oct 29 at 3:21
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As either editor or author, I wouldn't mind you mentioning other journals if you think they're more appropriate. I would also be transparent and concrete about why you think the paper is not appropriate for the top journal. A rejection stating "this is a strong paper but not strong enough" can really burn if it feels arbitrary. You could look at the last 10 papers in the same field published by the journal. If they're all stronger than the current paper, the author will understand the rejection better.

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    And, yet, in my experience (as an author and as an editor) most quick opinions do not provide such an explanation.
    – Moishe Kohan
    Oct 29 at 3:05
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    True, I was assuming a full referee report.
    – Stefano
    Oct 30 at 4:06
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You can simply suggest in the referee report to consider slightly lower category journals. But don't name any specific journal for example. I believe there is a downside in suggesting other "specific journals", because the other journals might not send the paper to the same referee(you) (unless otherwise) while the new referee might not find it enough interesting paper (there is a chance) which will end up with another rejection. The author will be upset. The best way to write "the work is something interesting that deserves to be documented somewhere but this journal is slightly higher ranked against the quality of the paper." Now it is the editorial decision to accept or reject the paper.

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It is the editor's job and responsibility to assess the article's suitability to the journal. As a referee, you are supposed to help the editor by giving your expert technical opinion on the correctness and interest of the paper. You need not write that the paper "falls slightly short", and even less recommend other journals.

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    I am not sure if you work in mathematics, but this is explicitly false for many mathematics journals. I have been asked specifically by editors to give my opinion on whether the submitted paper should be published "in a top $n$ journal".
    – Stanley Yao Xiao
    Oct 28 at 8:18
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    In academia, it is quite common that people ask you to do unethical or improper things. This is a mildly improper case of someone asking you to do what should be their own job. In this case, fortunately, there is no risk in not complying.
    – Sylvain Ribault
    Oct 28 at 17:49
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    I concur with Stanley's comment. I have been explicitly asked about suitability to a journal by many different editors. And I have been recommended journals several times in papers of mine when refereed.
    – Martin Argerami
    Oct 29 at 0:46
  • I agree with the sentiment of this answer. But referee vs editor duties are a matter of convention and subjective preference. "Falls slightly short" does feel to be splitting hairs a bit, but it's a subjective call to make. The editor could still choose freely to publish it, or reject it in the face of a positive review.
    – jdods
    Nov 3 at 10:07

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