What shouldn't go in your compost bin?

I have several dialeks and I've recently filled up one mainly with weed roots. Lots of couch, docks, dandelions, nettles and buttercups but nothing anywhere near flowering. I didn't think it would be of interest to rodents but last time I put some in I noticed a mouse had been gnawing a dock root. It will likely be some time before it is compost but I'm not in a hurry for it. when I eventually come to ue it, I will probably spread it thinly so if any roots are still alive, they can be picked out and put back in with new stuff.