The coolwwwsearch.leftovers is just a false positive by SpyBot . All of the coolwebsearch plugins are just browser hijackers , meaning that they tell your system to go to their page when you open Internet Exploder™ . Nothing to worry about....I don't know where you read they are "very nasty" but that is not true , they are merely an annoyance , although they do root themselves in your registry and try to broadcast back to themselves all of your web activities . But as far as ruining your computer or even messing things up , they simply aren't that kind of pests .
If you are on XP always disable your system restore and THEN scan because alot of these pests root themselves in the restore folder and will come back immediately even after being "removed" by Ad Aware etc. Then turn System Restore back on and the pests will be completely gone . Also make sure you clean out your temp files , especially the system restore temp files , before and after a scan .
Do yourself a favor and end the constant cycle of ad and spyware and go get Opera (my choice) or Mozilla's Firefox . Using IE these days is an un-needed liability , and it is simply unsafe .
F~