Noisy AI Mod 3A?

I've now come across a Mod 3 and two Mod 3As, including my own, that are susceptible to what appears to be ground hum in some systems (but quiet as a mouse in others). Moving the preamp and wires and cables around seems to work in reducing but not eliminating the hum. Lifting the ground on various parts of the system or replacing the tubes doesn't seem to help. Any solutions out there?
Some of them, mine included,pick up vibration from their own transformer. You can play with its positioning, put something on it or under it, or send it back if its under warranty. I also had a ground hum problem. Three things have eliminated it. 1, Different amplifier; 2, shielded cables between the preamp and amp, and 3, plugging the preamp into a completely different circuit.
Oh, I should have added shielded connectors with a WBT-like connector. The AI sockets or whatever you call them seem to be slightly smaller than standard, and sometimes I think a less than tight grip will cause a hum.
These things are extremely picky about tubes as well... Make sure you research tube changes... For your problem, you may want to try cones underneath the unit in both directions -- tubes selection combined with the chassis noise of this thing or other components may be amplified in a microphonic nature. I had a friend that went through this and found his 'fridge on the wall behind the audio gear was creating enough mechanical vibration to disturb his AI Mod 3. His fix was isolation (zoethecus stand & cones under the preamp) and different tubes that were less microphonic.
J_k brings up a point I forgot to mention. Anything else plugged that's plugged into you electrical system could cause a problem. I forgot about that and when my speakers started humming and buzzing last night, couldn't figure it out until I unplugged an old tuner I had just plugged in. Interconnects didnt matter, it was the power cord or the lack of grounding or something. Tubes can make a difference, but I have noticed that different units will hum or not with the same type of original equipment Sovteks.