As mentioned else where I changed my speedie bars for m bars which are shorter and in a very slightly rotated down position the wobble can hardley be felt. but let go of the handle bars just the same wobble as with speedie bars.
I suspect the mbars put more weight (from the rider)on the front end thus reducing the wobble effect even though it is still there at the same amount.
Not a cure but I love the bars great comfort for me.
Also just put on a 19 tooth sprocket very different let you know how it goes.
