[Titens]

Monster is a masterpiece that fits well in all your requirements. It's also way better than the two animes you named.
You could also try watching 12 kingdoms... it's a bit boring in the beggining, and it's technical aspects aren't that great,but it's one of the animes with best story for sure, and also one of the best anime's i've seen overall. Also, no mechas and almost no comedy in it.
Of course, there's also Full Metal Alchemist if you are looking for good stories (it's my n° 1 anime in that aspect). Even if this one has a lot more comedy in it, it is not filled with it... and even if it was, you should watch it anyway, since it's in my top 5 even after I've watched more than 160 anime series.
You can also watch Kaiji. It's an ongoing anime (still airing), with weird design, but a fantastic story so far. Might not look apealing at first, but it fast turns into something you can't stop watching.
Hmmm, there's also Eureka 7, but... o well, this anime does have a lot of good comedy in it, and it also have mechas (but unlike what you have probably have seen, they only have a secondary place to tell an amazing story), but it also has a serious story, and it's so good in every aspect that it's one of my 3 all time favorite animes. I know you'd be surprised if you watch it... after all, is so much better than blood+.
Finally, there's also trigun, shigofumi, Legend of the galactic heroes, Mushishi, etc...