I operate a 1977 Decthlon CS for tailwheel conversions and aerobatic intruction.
I had a lot of problems with shimmy - my previous aircraft, a super decathlon, had to be welded for that reason.
I found there was a gap/clearance between the tailwheel assembly and the spring, which allowed the complete tailwheel assembly to be able to move sideways, pivoting around the bolt.
I put a sheet of cobber in between, which filled up the space sideways, and tightened it hard.
After this I have had practically no shimmy. I recal only once where a student made a poor crosswind landing and pulled the stick fully back - other than this one incident, no shimmy so far.
I have experimented with less air pressure - no help, only result was a blown tire.
I teach the students, when we do 3 point landings, to leave the stick where it is when touching down and only mooving is aft slowly
Regards Lennart Wahl, Aerobatic instructor, Denmark