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I'm applying for graduate school in a hard science this year, and most things on my application are pretty good so far. Two of my letters should be strong, but regarding the third one, the professor told me in the interest of full disclosure, that his letter will be a positive one, but certainly not the best he's written. This particular researcher is well known in his subfield, which isn't the field I'm applying to, but it's not very far away either. I've taken many of his graduate courses, and also did an independent reading course with him. The graduate courses went pretty well, but the reading course didn't unfortunately, (mostly due to a difference in style) and as a result of all this interaction, he knows me well, and he thinks I'm a good but not great student. Now I'm really hoping I can get into at least one of the better schools on my list, and it's insanely competitive, particularly in my subfield.

Another option of mine is asking another professor who doesn't know me that well and is in mathematics instead than the hard science I'm applying to, but he certainly thinks I'm a top student, since he was responsible for many of the math awards I got and I did really well in the one class that I did take with him.

Q: Would having two great and one good letter hurt me at the top places? My impression is that students who get admitted to top places have their professors say that they're the best student they've seen in many years, and not having such a letter could result in rejection. Which recommendation should I go for? Is it advisable that I even do both and send in four letters?

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I think professor "you're good but not great" is doing you a great service by letting you know in advance that his letter will not be one that you want in your application. If you are applying to an insanely competitive program, then indeed such a letter would jeopardize your application. I've done graduate admissions at the 50th best math department in the US, and we can do better than "good but not great".

A letter from someone in an adjacent field is definitely not as good as a letter from someone in your field, but getting a letter from someone who was responsible for "many of the awards" you got is certainly strong. The sentiment that you have award-winning mathematical skills should be a positive one on an application to graduate school in the sciences.

I would definitely switch the letters. Also remember that the first professor really helped you out. It is not the sort of help that is worth an effusive thank-you on your part, but it is worth keeping in mind and perhaps remembering to do for someone else someday.

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    Thanks for your answer and I've just sent an email prof 2. When I asked the first professor initially, he said I should focus on the schools rated from 10-20 and said that I have a very strong chance of getting into them. So he certainly thought well of me, perhaps just not top 10 material. My other reason for considering still sending his letter was that my other two should be strong, and I thought that it would have been acceptable to not have all three letters be glowing. What would be your thoughts on sending his as a fourth letter?
    – user24542
    Nov 20, 2014 at 17:32
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    "When I asked the first professor initially, he said I should focus on the schools rated from 10-20 and said that I have a very strong chance of getting into them. So he certainly thought well of me, perhaps just not top 10 material." This conveys a slightly different impression. Perhaps not top ten material is rather different from "good but not great". As I said, I have done graduate admissions at about the 50th best math department in the country. When we get letters which describe the applicant in these lukewarm terms: e.g. "recommend" versus "recommend strongly", it does not bode well.
    – Pete L. Clark
    Nov 20, 2014 at 17:52
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    You sound like you may not be completely clear of what the professor thinks of you and/or what he meant. The key question is: why has he chosen to disclose to you that he would give you a sub-optimal recommendation? I don't know why anyone would do this other than to suggest that you should look for stronger recommendatins elsewhere. If I thought a student would be well placed in the 20th best program in their field, I would certainly write them a very strong letter and I would not be warning them that their letter might not get them into the top ten. No one letter does that.
    – Pete L. Clark
    Nov 20, 2014 at 17:55
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    Also, you described that you reading course you took as "not going well". That's quite negative. In terms of it being "acceptable not to have all three letters be glowing": that's a strange remark. Yes, it's acceptable but it may not be enough to get you accepted. Are you really not aware that top programs (not just the top 10) mostly to exclusively accept candidates whose applications are superior in every way? (Perhaps you don't fully understand what "insanely competitive" means?) Anyway, no, it would not help to submit an additional letter which is worse than the others.
    – Pete L. Clark
    Nov 20, 2014 at 18:03
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    Pete, I think the warning may not be a red flag, so much as a reality check. Say I'm writing a top-20-but-not-top-10 letter for a student (i.e. the last sentence of my first paragraph contains the phrase "top-15 department" or equivalent). Certainly there is nothing about this situation that would be cause for warning the student; I have a high opinion of them and will write a strong letter. But if I then learned the student was only applying to top 10 schools, I would feel the need to clarify that my letter is not going to make that happen. I agree with your overall advice though.
    – Tom Church
    Nov 20, 2014 at 19:40
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"Not the best I've written" is probably a huge understatement, and he's letting you down easy. Pretty much all letters of recommendation are positive ones, so he's basically saying he'll write you a bad or mediocre letter.

I would definitely go with the one who doesn't know you as well but will say good things about you. I think people understand that most undergrads aren't going to get to know three different professors on a super personal level. But it would be bad if you did get to know professors and they said bad things about you.

Besides, it's nice to have someone who can attest to your mathematical ability, since that trait is strongly prized in many of the hard sciences.

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I can tell you from personally witnessing the contrary that even a professor who writes your recommendation letter can't really predict whether or not you'll be admitted into his own department correctly. So don't expect that to jeopardize your application.

That said, if you think your second recommendation will be stronger then send that one in instead of this one which you know isn't great; I don't see the benefit of not doing so.

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