[K.Wilson]

Stearing wheel shimmy can sometimes be difficult to track down as there are many variables.
Assuming that the wheel bearings are adjusted correctly (not too loose) and that the brake rotors are true, it leads you to the tires.
Not all tires are created equal, some have significantly more runout (both lateral and around) than others. A good tire and wheel shop will have a "runout gauge" (a largr dial indicator with a small wheel that will roll against the tire). With the tire and wheel mounted on the car, and the wheel off the ground, the runout can be measured on the side wall and the tread.
If an runout of greater than .200 or .250 inch is measured on the side wall you may want to think about replacing the tire as there may be a ply seperation.
If the tread has a runout of more than .100 inch you may want to true up the tread surface. This is accomplished with equipment that turns the tire and wheel assembly and "grinds" the tread surface to take off any high spots.
If all else fails you can add some additional toe-in, as little as .125 inch will add enough tension (tire scuff) to reduce the shimmy. Tire wear will increase, but the shimmy will be reduced.
Keith