If you look through a magnifying lens at the rust, you will see that it looks like a flower. It seems to cover much more area than it ACTUALLY does.
Spray the rusted surface with WD40, which will penetrate the rust. You can also use any penetrating oil, like Kroil, Liquid Wrench, etc.
Now dip your 0000 steel wool into a heavy motor oil, and LIGHTLY rub the metal surface. Stop frequently to take the oil and iron oxide off the metal surface with a soft rag, so that the oxide that is those "flowers" will not scratch the metal, either. Re-oil the barrel and continue to lightly rub the surface with the steel wool.
I have also used wooden sticks to burnish rust off metal, provided that the surface was well soaked in oil first. Go SLOW! Clean often! Re-oil often ! All this is to protect the finish under the rust, be it "patina" or some kind of artificial coloring.
I have used this technique to remove lots of flowers of rust on a modern, Blued barrel, where any scratch would have jumped right out at you. The oil helps the oxide(rust) FLOAT on top of the metal, once broken free, leaving a very tiny pin hole in the metal.
In the case of the factory blued finish- really blue/black, I heated the barrel up to about 400 degrees, and wiped on some "cold blue" paste, which sizzled as it touched the metal. Then cooled the barrel and cleaned off the residue under a faucet, dried the barrel, and then heated it up again.
This time, I sprayed the barrel WD40 which burned and smoked, and fumed a lot as I sprayed it on. It also darkened the barrel, and those small spots where I had touched up the bluing.
Heating opens the pores, so that you get a deeper oxide in the barrel surface. I let the barrel drip over night, covered with oil, so that the black color would set into the pores.
The next day, I wiped down the barrel, and inspected it closely in natural sunlight. Because I knew where the pinholes were, I could still find them. But, when I returned the barrel to the owner, he could not see them, unless I pointed them out to him. He was delighted with the restored finish.
There is also a New product out called "Evaporust" which really works well. I would use this on any rust on an original antique firearm, before using any other technique, including the ones I describe using above. :hmm: :v :thumbsup: