USA car rental: insurance 'extras'.

On my last USA trip in Feb 2010 I hired a car for a week from
Enterprise in Encinitas, California. At the last minute as I was being
handed the keys I was asked if I was covered for various extra insurance
provisions. One was collision damage waiver, or something along those
lines, and the other I forget. But the bottom line was that, because I
wasn't 100% sure, I'm sure I ended up paying excessively for redundant
insurance.

With another USA holiday planned, I'm going to call my own UK insurance
company (Saga) to see exactly what I am and am not covered for in this
context. But meanwhile I'm hoping someone here can sum up the basics for
me please. The key question is: am I likely to be ALREADY covered for
these things on a reasonably comprehensive UK car insurance policy?

--
Terry, East Grinstead, UK