E65 shimmy

[bennyboydurham]

I know that the E38 is famous for shimmy at higher mileages but I was wondering whether anyone had come across it in the E65? I've been driving my wife's Z4 for a while and getting back into the 7 today I noticed a little bit of shimmy between about 45 and 60mph. Over 70 and it's barely noticeable. Over 85 it's as smooth as silk. There's no shimmy under braking and it's hard to describe where it's coming from - definitely not through the wheel although that doesn't rule out the back wheels. I tried sticking it into N on the move to see whether it disappeared when not under load but it didn't seem to make any difference. I know good men have been bankrupted and driven to mental illness trying to cure big Bavarian shimmy but I'm just wondering where to start.

Wheel balancing first off, perhaps? Are there any other things I can look at that won't bankrupt me?

[roofer]

If its doing it through a given speed range, balance would be my first port.

[PJ S]

If not wheel/tyre imbalance, then bushes & driveline would be next for checking to narrow down.
Can you tell if it's front or rear end?

[bennyboydurham]

Bushes might be worth a look. Could anyone give me a ballpark figure for getting them done?

[bennyboydurham]

Interesting - thanks for all the advice. I did get an alignment check done and everything was fine. I might revisit the wheel balancing again as I've heard that it can take a bit of getting right. Not sure I can stretch to a new set of wheels but I'll look into it. Thanks all.