Jan Heine and Mark Vande Kamp wrote an article, Curing Shimmy on a Bike in Bicycle Quarterly, Volume 6, Number 3 (Spring, 2008).

They believe that frequently the problem is caused by the head tube upper and lower edges not being perfectly parallel. They contend that on a standard ball bearing headset the balls on one side tend to run looser than those on the other, causing shimmy. On Mark's Ti bike that had a very strong shimmy under certain conditions with a Chris King headset installed, they swapped out the Chris King headset with a Stronglight needle-bearing headset. Stronglight headsets are different from all others in that the bearings align automatically, and thus compensate for imperfections in the facing of the head tube. After they swapped the headset, Mark tried to induce shimmy as he had before, but the bike no longer shimmied. After numerous attempts, he finally got the bike to shimmy briefly, but instead of continuing until Mark put his knee on the top tube, the shimmy now attenuated on its own within a few oscillations.

There's more to the article, but that's the jist of it. When I read the article in 2008, I realized I had never had a shimmy problem under any condition while riding my '87 Paramount with the OEM Stronglight A-9 needle-bearing headset.

YMMV.