I have rented cars in Greece, UK and NZ. Each time the rental includes accident damage with a large excess/deductable. I have found that by paying a bit more I could get cover for the excess. This came in habdy in NZ where the basic insurance did not cover windscreen damage and, yep, the screen got hit by a stone which left a star chip. This was picked up by a check of thje car when I retuirned it but, by having the extra cover, I did not have to pay for a new windscreen. Another time in Wales I scraped a rear fender against a stone wall while parking in Caernarfen. I didn't notice that this had happened as the fender/bumper was made of plastic. The damage was picked up on return of the car at Heatrhrow and I was saved from having to pay a hefty excess.