I have Tein S-tech's fitted to my jazz and they are very good, although my dampers need changing now.
No beacause of the springs, just that the car has don 145,00 miles.
The only option of new dampers is Honda, bilstein or Monroe. Unless you get some from the USA.
The car will still understeer if pushed hard, but lowering it does make a difference. No had much problems with it grounding out.