The best thing I invested in for my lasagna beds & compost bin was a paper shredder. Junk mail (non-glossy paper) , plain tag board, etc. becomes brown matter for either location. But be sure to either top it with another layer or wet it thoroughly because you don't want shreds flying around. If it's windy I put the paper in a bucket of water to soak before trying to dump it on the pile. Learned that the hard way.
I also keep a small trash basket for tissues & napkins only. Every little bit helps. I've even read to use dryer lint from cottons. But I haven't done that one.
Making a new 'lasagna bed' for perennials?
