If you want even greater security for material you shred, I suggest two ideas.
#1 Always mix the material in the shredder and empty part of it into the trash, leaving maybe a third.
This will mean that unless someone gets your trash ever week, they are not likely to get a full document. I imagine that would be very frustrating. :-)
#2 Got a cat or dog? Add the you know what to the trash back with the shred. It would discourage me.
I do follow my first suggestion. Not that I really think I need to worry, but I do get a little smile thinking of the possibility of some homeland security team working weeks trying to figure out what is going on.