In Pandora, I have several "radios" such as Coleman Hawkins Radio, Gene Harris Radio, Count Basie Radio, etc, etc. Each time I play any of these "radios" it starts off with the artist I like such as those named above but after 2-3 tracks Pandora in its infinite judgement chooses tracks that are LIKE Coleman Hawkins/Gene Harris/Count Basie but are NOT exactly the artists of my specific choice. The music is really not what I like/want to hear & I get pissed off & turn off Pandora!
Well, this is exactly the point of Pandora, i.e. to play similar artists. If you only want listen to specific artists then Pandora is not for you. I love Pandora for exactly the reason that you don't like it, because it introduces me to new artists and music.
As Mitch4t suggest, you should consider either Rhapsody or MOG.