steering wheel shimmy

03 LS sport

have had the tires balanced twice, and still there is a slight
to kind of harsh steering wheel shimmy that is very mild at
50 or so getting pretty strong at 70 mph then smoothing out
at 80 or so. the tires and wheels are new and the suspension parts don't
seem to have any play. (the shimmy occured with the original wheels as well.
the tires were installed just before i bought the car so i dont know if the car
was doing it with the previous tires).

could the inexpensive tires be the problem?
will i need to replace bushings or bearings?

any advice would be helpful . thanks J

It is very possible that the tires are the cause. Even if they balance out, they could have excessive lateral runout (out of round), or excessive road force variation (can only be measured on a tire machine with that capability). Have the tires checked for excessive run out.

I've had this problem before. Having the tires road-force balanced cured it. Not many places have the machine for that, so you may have to shop around.

I've also heard of someone who have a brake rotor out of balance that caused the same issue. (Not warped where the car shakes when you used the brakes, but unbalanced so that you get a constant shimmy at higher speeds.)