AR ground issue

I'm getting the non-grounded hum on my AR turntable. When I attached the ground wire to the pre-amp it significantly diminished but did not disappear completely. I've found it gets worse when the tone arm is in position to play and gets a little better when the arm is on the rest.
Any suggestions what the problem might be and/or how to fix this?
Have you tried using a phono specific pre-amp?

Synesthesia Studios
What phono cartridge are you using? Some brands, like Grados, are not shielded and can pick up hum from the AR's internal motor.
Also, are the interconnect cables shielded? Especially important if using a tube pre-amp. Hope this helps!