Thanks for all the replies. I have some things to try now. The rifle is a Tikka Whitetail Hunter, which comes with a free-floating barrel from the factory. I need to shoot it some more to make sure it' s the rifle and not something else but I think I' ll try the tip from 8mm/06 and see what happens.

If that doesn' t work I might have to glass-bed the action (comes with a plastic piece that slips into a slot in the stock, must be there way of bedding or something). Anyone bed their Tikka WH yet?