I had a shocking bar wagging problem in my KTM 990 SMT when I first got it. Anything above 60 mph threatened to turn into a full-on tank slapper, even when I was gripping the bars. I tried all sorts: fiddling with tyre pressures, suspension settings, removing the hand guards, even drilling a large hole at the base of the screen in case it was wind buffeting. Eventually someone on the old Supertwins KTM forum asked me what tyres I was running. Told him Metzeler Z8s and he said I bet that's the problem. Get rid of them and fit Dunlop Roadsmarts. I did and he was right. Instant rock-solid stability. It's amazing what a difference the right choice of tyres can make.
Admittedly the 990 supermotos were very fussy. Get them just right and they were sublime. Deviate even slightly from the optimum set-up and things went very wrong very quickly. Even so I've never seen such a dramatic change just from fitting different tyres.