This has taken me some time to figure out, but this seems to work without any errors or leftovers from Unity whatsoever. It also removes the possibility of choosing "Ubuntu" at login by fault, and booting you into a desktop that won't start. YOU FOLLOW THESE INSTRUCTIONS AT YOUR OWN RISK!
I have just copy-pasted this from my Tomboy notes, so it's written in short-hand and should therefore not be considered beginner-friendly, and SOME knowledge of the terminal/command line is necessary. Anyway. here it is:
Log out and choose Ubuntu Classic after choosing your username.
1. Software Center -> Remove Unity and Unity 2D
2. Synaptic -> search for "unity" and purge everything with unity in it
3. CompizConfig Settings Manager -> Window Decoration OFF
Window Decoration -> Change Command to gtk-window-decorator
4. Terminal -> sudo apt-get autoremove && sudo killall unity-window-decorator && sudo apt-get install fusion-icon && fusion-icon
5. CompizConfig Settings Manager -> Window Decoration ON
System -> Settings -> Start Up Programs -> ADD -> Name: Fusion Icon -> Command: fusion-icon --sleep 5 -> Comment: Start Fusion Icon with a 5 second delay on startup
6. Terminal -> sudo rm /usr/share/xsessions/gnome.desktop
7. Terminal -> gksudo gedit /usr/share/xsessions/gnome-classic.desktop -> Change to Name=Ubuntu -> Save -> Exit
8. Terminal -> sudo mv /usr/share/xsessions/gnome-classic.desktop /usr/share/xsessions/gnome.desktop
9. Terminal -> gksudo gedit /usr/share/xsessions/gnome-2d.desktop -> Change to Name=Ubuntu (No Effects) -> Save -> Exit
10. Right-click the Fusion Icon in the systray and check that Select Window Manager is Compiz and that Select Window Decorator is GTK Window Decorator