Hey !
I've encountered this problem too. In the tags that Itunes proposes to fill, everything is similar and right. Nonetheless, I have two Count Basie in my Artists grid.
Why solutions exposed above does not work ? Because the problem is deeper, it is a problem of tags disharmony. The tags Itunes allows to see are the first necessities needed. However, a music file can contain much more metadata in it, kind of invisible part of an iceberg.
In order to fix this problem, you need a program (I use Kid3, it works perfectly and allows to manage a lot of files simultaneously) that can show you all the metadata. Then open all the music files affected (if you have two Count Basie in your Itunes, open all the Count Basie directory in Kid3), select all the files, just erase the tags you think you don't need (not only the information but the all fields of tag). Doing that, you will remove the potential conflicts that put Itunes in mess. For instance, I think I understood that if a music file has two fields called Album artist or has one field called Album artist and another one called "Order of album artist", it creates a conflict with which Itunes can't manage.
Thanks to Kid3, I have edited all my tracks of Count Basie in such a way that only the basic tags Itunes asks remained. Then I've just imported again all the tracks in Itunes and guess what, I got the very unique Count Basie as artist of many tracks !
Hope I've been clear.
Good luck !