The rubber of my first handle was damaged. May be this was due to chemicals
of the ground that entered into contact with this rubber.
XP exchanged it and the new rubber (right part of picture below) seems to be more resistant.
Nevertheless, now I am protecting the handle through following solution:
As alternative protection solution, you can also recycle some packaging material:
This is my final optimised realisation:
11/10/2010: big thanks to Johne for his idea to use protections for bicycle handlebar, see next pictures !