I scrub my chamber three to five inches deep with a nylon brush and CLR or carbon remover for ten to 20 strokes, leave it in the barrel for ten minutes, and then remove it with rimfire solvent from Veldt or Bore Tech. Give the barrel five strokes back and forth, as it is not necessary to scrub a rimfire barrel too much. Give it three wet and dry patches and we are done!
Take care when storing your rimfire rifle after shooting. Do not leave the barrel fouled