Gary Fisher Kaitai suffers from handlebar wobble at moderate speed with 10lbs on rear rack
There are a few things that could help the shimmy, but there is no real silver bullet. 

Typically the shimmy is a function of head tube angle, top tube length and frame (specifically top and down tube) elasticity. Jobst Brandt describes it best in this article so I won't get into too much detail on the whys. There are a few things that reduce or negate the shimmy that have worked to varying degrees for myself. 

1) Knees against the top tube. Squeeze the top tube with your knees. 
2) Stem length. Sometimes a longer stem might help out. Very frame dependent and you would not want to change your fit imo. 
3) Handlebar bag. Distribute some weight to the front and see if a handlebar bag can help overcome the gyroscopic forces created by the wheel.
4) Switching to a set of tyres w/ more 'tread' (ie. knobbies). I haven't tried this but the jobst brandt article indicates this could work. 

The Kaitai is pretty unique in its long top tube, exceedingly short head tube and relatively steep head angle. This also makes the bike a 'tough fit' for the majority of people.