I see on many a post about using steel wool to restore, repair, clean, remove something on firearms. I would suggest you use BRONZE wool instead and you will get great results and not discover you ruined something you meant to fix instead. Any good hardware store should have it.
Just a suggestion....not carved in stone.

Hmmm, I've been to two goat ropings and one county fair. How come I never heard of this before?

I now use the ultra fine ScotchBrite type pad. It is a lot eaiser to fine. It won't leave particles that will rust like steel. Which is another reason not to use steel wool.

Pecos...it is cause you never went to a windmill fixin...they use it on sailboats all the time too. Like the other poster said...won't leave rust fibers around.
Mine says ISW corp, box 1767, Springfield. Ohio 45501...8 pads, fine...for marine and industrial use.
Try it...see what you think. Will take off the rust and keeps you from cutting the blue you want to keep on.

Brownells have it, and do indeed claim it doesn't damage the blue. There may be some chance of leaving bronze traces on a textured finish, that will interfere with rebluing. The Scotchbright pads, especially rotary ones, are excellent for many purposes, but will remove bluing.

Caledonian...thanks for coming to my rescue...I think some thought I was crazy (ier)

You can use one of the various copper bore cleaners to remove any residue the bronze wool might leave.

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I know the next rifle will be perfect.......

Steel wool will not damage a blued finish either. The rust on the steel wool will. It is abrasive. Rinse the steel wool often with spray lube. Scotch bright will certainly damage the finish. Amway stainless steel "Scrub Buds" are the best for the remove the rust and keep the blue job. Scrub Buds look like very coarse steel wool. They look like they would destroy the finish, but they don't. I think the coarse turnings that make up the material are so open that the rust particals don't build up to the point that they can do damage. This stuff is also the best thing for rusty bores. Wrap it around a brush. It will grab the rust and pull it off the surface with out damaging the remaining steel.

"I think some thought I was crazy (ier)"

Fighting......the......urge......to.....comment...

Longbob...it could be a very expensive comment!

Perhaps I was a bit hasty. I haven't picked up my TuffSak and I did promise to be nicer to you after you did me that favor. This is hard.