There is definitely a difference between hardtop on and hardtop off. It seems better with the top on. However, I think any improvement will be minor and it is more a question of perception. Maybe the hardtop dampens the scuttle shake somewhat; it must do, surely? But I can't believe it adds significant rigidity. I don't know...

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JJ Rodger
2013 G350 Bluetec
1999 SL 500
1993 E300 diesel T
1990 190