Tag all the tracks in the singles album as compilation. Then in iTunes Edit/Preferences/General check the "Group compilations when Browsing" checkbox.
This removes artists where all their tracks are tagged compilations from the artists list. But if you have artists with some tracks in compilations albums and some tracks not in compilations (their own albums). Then the tracks on the compilation albums will also appear under the artist aswell in compilations.
This is very clever and I don't know of any other player that does this. Its one feature of a couple of features that would make me get a iPod over other players.
I think the "Artist Album" is what appears in the Artist list. Not "Artist" if theres both. So if you are seeing funny artists in the list check the "Artist Album" tag.
I don't have an iPod other than a Shuffle so I don't know how this works when you synch with an iPod. I only use iTunes (along with MediaMonkey) to clean up my tags. As I usually use filetree myself.