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Okay, given that we have similar tastes (I loved Gantz, Death Note, Rainbow, Darker Than Black and Ergo Proxy), I think I'm in a position to recommend some amazing anime. I'm not going to follow your really tight rules though, good serious and deep anime are few and far between - limiting yourself to a very narrow selection will leave you disappointed.
Wolf's Rain - I know you stated that it seems fantasy'ish and what not, but you are doing yourself a disservice by not watching this very deep and interesting anime.
Gankutsuoh - Futuristic Count of Monte Cristo. Great anime, but it takes a few episodes to get used to the very unusual animation/texturing.
Berserk - By far my favorite anime. Starts off as a your typical sword play show, but evolves into an epic story of good, evil and free will.
Claymore - Hesitate to mention it. I thought it was really enjoyable to watch, but in the end this is a mature action anime with an interesting story, rather than a story anime with good action scenes.
Basilisk - Same as above.
Some other suggestions of what I have liked:
Last Exile
Evangelion
Full Metal Alchemist - This is an odd anime. Alternates between being a light hearted action anime and a stone cold, brutal drama.
That's all that I can think of right now. You really can't go wrong with any of the anime I listed. I personally enjoyed Berserk immensely, even more so than Gantz and I think you should at least give 5-6 episodes a try.
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