In reply to matthew jones:
Don't tie it, the knots slip at relatively low loads (plus it's messy). With rigid cams and cams having a solid sling attachment point (as opposed to a wire loop) you can either push a loop of thin sling through the hole then clip both loops or form a neat hitch. Just beware of sharp edges in areas the sling didn't previously contact. For cams with wire loops just clip a 'draw into them or replace like for like materials (eg push a loop of 30cm 12mm through a DMM 3CU and clip both loops). I wouldn't girth hitch to the wire and you should be wary where fatter nylon tape was used initially, it's possibly to prevent wire or sling failing prematurely.
Don't do what you're not happy with and do consider getting them repaired by the manufacturer, it may be the cheapest neatest solution.
<edit> I forgot to say, I re-slung my old Camalots and flexi-friend like this with 8mm slings doubled through the hole, both loops clipped. They're neat and still catch falls. Can't say much more than that about them.
jk