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Specifically articles & essays (ie 15k-25k words). Possible, or will you be disqualified at the CV review stage?

HYS upperclassman if this matters. Otherwise, my "CV" is irrelevant.

If that's a no-go, what other avenues are there to get published? I.e., avenues that are well known, selective, and known to be selective?

Some journals take student work, and some don't. You'd have to check with the journals that interest you.

I'd speak with faculty who work in the subject area of interest. They might know of non-law school affiliated journals (run through ALI, for instance) or lay publications that could adapt a legal article.

There will also be other journals at your law school that accept student notes or comments either in their print edition or their online edition (some journals at my school for example have their online sections cached to westlaw/lexis so they can be cited as reputably as the print edition). We receive email blasts and other circulated information from the journals offering this type of resource.

I received 2 publication offers as a HYS rising 2L for an article I wrote (one secondary, one TTTT LR).

My school paid for submissions, so I blanketed every journal that did not specifically say no student submissions. Got a lot of auto dings for being a student, but it appeared from the feedback I received that a lot of journals at least considered my work.

Good luck!