What do you do with old bank statements?

I’ve accumulated a pile of old bank statements, credit card statements, and the like. Assuming that there’s no paper shredder, what do folks do with these? During summer grilling season we burn them as tinder, but it’s winter now and I don’t want to save piles of paper for several months. I don’t want to just tear them up to throw in the recycle bin, as usual, because I’ve been assured that this is unsafe.