I've switched completely from steel wools to the non-woven abrasives. They are available from most woodworking shops and are fantastic. They don't shed like steel wool (no more worries about pickup magnets!) , and they can be washed and re-used.
Typically the colors roughly correspond to steel wool grades.
Green = 0 steel wool
Maroon = 00 steel wool
Grey = 0000 steel wool
The white is almost too fine to be of any use. I usually skip it and go straight to the buffer.
Mirka makes a similar product they call Mirlon, it comes in some course grits and two very fine grits. The fine grades are an excellent product, with a very fast cut, but it does cost substantially more.
On some of the other forums people rave about using micro mesh products. There is nothing wrong with them, but in this application (knocking back to satin) they are overkill, particularly when the non-woven abrasives work just as well at about a tenth of the price.