I usually have three piles going: My "official" one, that I enclose in the cylinder and in which I compost kitchen scraps and the other good stuff, a pile for brushy things that I am too lazy to cut up for the official pile, so it just piles up there, and that is mostly yard waste and larger trimmings, and the third pile is where I dump things like thorny stems and grass that might spread and things that propagate from runners a bit too easily.
That third pile is the stuff most people want to throw out, but I try to save as much biomass as I can to put back into the soil, and I have found that if you leave it there long enough, it does break down.
No attention, or notmuch attention, is paid to piles two and three. They are just storage but eventually they do become compost!
If you don't have much kitchen waste to compost, it's easier to set something up, in a way, because you don't have to manage it as closely to keep smells from developing and unwanted varmints from taking an interest.
I just got a couple good pictures of my current compost and will post those soon.
