MX5's floppy chassis

[joetait]

My wife has a mk2.5 mx5 (10th anniversary 1.8 6spd) which has loads of chassis shake over bumps. Is this normal and are there any effective bracing methods around? she used to have an MR2 roadster before which was infinitely stiffer and handled much better. The car has done about 60k now although she bought it with ~30k /FSH a year and a half ago and it has always felt like this.