I don't like using steel wool. The little bitty pieces get everywhere and rust everything up. This is in an unheated outbuilding where my reloading & shooting stuff stays. Years ago, I started using Scotchbrite pads for stuff like this. The finer you want it, the more USED UP it needs to be. For cleaning dies - carbide or carbon steel - I remove whatever stem the die has, then wrap a nylon brush with scotchbrite for a snug fit. Run it in & out of the die several times, while spinning it with a drill - run the drill in reverse so you don't unscrew the brush from the aluminum ferrule. Then a spray of crud cutter etc, and a final spray of lube (I use Tetra) , a wipe off, reassembly, and you're done..........Bug.