Don't know what uses you're putting the 0000 into. There has been much discussion over on the gun forums, warning about most modern steel wool when used on wood (gunstocks).
Seems it is manufactured in a very large foreign nation to very low tolerances. The strands have micro barbs on them which can embed into the wood and later rust.
Based on these warnings, I moved all of my fine wood "sanding" over to synthetic polishing pads which also come in varying degrees of fineness. Most hardware stores seem to carry them.
Oh yeah, they don't shed, splinter and deteriorate. Use repeatedly.