I have had the same problem, mine is a 2002 1200S,I have changed the tires and there still is a shake, I have had it checked out and according to Suzuki as long as I keep a good grip on the handlebars everything should be OK, they say it's a combination of the tires and the way it is built, I don't buy that, it didn't do it before so why now. There has to be a cause and I would really like a solution. I am now trying the Dunlop 208's. Any one have suggestions?