Over the past weekend I have made some interesting observaion that I would like to share with everyone. I have small vibration like everyone in here experienced at certain speed but right before Chrismas I went to discount tires for a quick air check and the vibration became before noticable.I had a theory that they over inflated the tires cause all the vibration over smallest bumps on the road so I went out and check the air pressure in the tires and they are all about 34+ in the morning. I let out some air so I have 33psi in the front and 32 psi in the rear. Most of the vibration/shake went away. Back to before the air check. Try out my method. It doesnt hurt. I still have little vibration but I can live with it for right now. I also notice a small vibration/body flex while shifting up/down gear in sport shift while the tires went inflated above 34 psi. Crazy rattle too

 

It seems you just made some kind of dashpot or damper onto your car... dealing with elements of tires surely would ease some of minor vibration... IMO...

 

At over 34psi the whole car would shake vibrate over every imperfections on the road. Very harsh ride. I cant explain it but just try it out. Maybe the suspension on the TL is too stiff it would get upset the whole car over every bump at higher tire pressure

 

I would agree with you. I have noticed that my car is particularly susceptible to even minor changes in air pressure. Keeping the tires at 32/32 like the factory says seems to work out best for me and my driving style. It can't hurt to check them every week and make sure they are inflated properly.