My first thought is my old school; NNPTC (Naval Nuclear Power Training Command).
When I went in, to even be considered to be offered the NFQT (the entrance exam for the Naval nuclear power program) you need to have an 80+ on your ASVAB, and then you have to have a raw score of 54+ on an 80-question test that covers things like trig, calculus, physics, and other such stuff. Do all that and they offer you Nuke School; second in the world only to Harvard Law on the list of “Schools that are hard to pass unless you have your shit together”. I refer to strictly academic schools here, and not stuff like SEALS training that has a prominent physical element.
It seems to me that that qualifies as “put[ting] a premium on smarts” and “military”.
@cazzie You are partly correct, but not entirely. I have too many ex-Navy Nuclear Engineer friends who required no further education to cross over for me to agree.