Neko Case is overrated, and you can do better Alt-Country than Jenny Lewis.
If you want a little more alt, check out the Jayhawks, Hollywood Town Hall and Forever the Green Grass especially. It rocks pretty hard, but it also has elements of classic more Alt-y stuff.
If you want more country stuff, check out Hank Williams III. Dude is just amazing. Get Risin Outlaw, and just be awed by the man.
Also dude if you like this genre of music at all, you owe it to yourself to check out Gram Parsons. I like ..And the fallen angels live, but all his stuff is good. He originated the genre, and he remains pretty much the best possible example of the genre.
Also many other bands, tell you about them later.