The 2cm long scratches on my BlackBerry screen bothers me already - even if it is not very deep, it is just in full view. So I bought a Displex Tube and polished it off. Only the scratch was even after 10 minutes Polishing not less, for the terror came after removing the polish: In so treated area, the display has become somewhat milky and no longer feels as smooth on. Due to the apparent rough surface become dirt adheres now even better (can also be super test with water: In polished section it bubbled significantly worse).
So I can only say: hands off! There's not only the money for the Tube away but you can think about how the damage is to be remedied now newly created to advance.