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I have two very strong letters from professors at my university. One the chair of the department from which I graduated, one a tenured professor. However, the latter never actually had me as a student. Rather, he was my debate coach/advisor and worked very closely with me for 2 years. Can I still use him as an academic reference if he can't attest to my actual classroom work ethic? Obviously, debate involves research, writing, etc., just not sure how this looks to the admissions folks.

Further, I have had two internships, both of which had lasted only 4 months. I don't think I have established strong enough relationships (regrettably) with my advisors to request the strong letters that I need for my apps. Will the two aforementioned LORs suffice? Thanks!

Adcomms know what happens within debate with the whole research and writing aspect. If you know that he truly wrote a strong LOR, then you will be fine.

Also, you already have these 2 LORs, don't get one from an internship you were at for only 4 months. The academic and debate one are better than a 4 month internship LOR. I was in the same position, I was going to get one from a Judge I interned for but his LORs was a generic template that he uses for all interns who ask for a LOR, which is something your internship spots probably do as well.