Elmer, I use a technique similar to what I am about to copy and paste below. Different people have different techniques, but they are all similar to this one. Sometimes they shoot several shots between swabs. The important thing is to get the copper fouling out and that means swab, swab, swab with a chemical bore cleaner to get the copper out (I use Shooters Choice). It is always easier when the barrel is warm so even after you have broken your gun in, it is always easier to clean at the range. Here is one suggested cleaning formatt. Search Google for something like "breaking in a barrel" for other ideas:
BREAKING IN A RIFLE BARREL
Machining marks which can fill up with copper when the gun is shot are left during the manufacture of rifle barrels. The purpose of breaking in a rifle barrel is to polish or peen these imperfections smooth with the barrel. When a bullet is fired over these marks, it tends to polish the machining marks, but at the same time, copper is caught in the ridges. If you continue to fire bullets down the barrel without cleaning, the barrel will continue to foul (collect copper). Fouled barrels do not shoot as well as clean barrels. With that in mind, here is a recommended method for breaking in a barrel.
1.Before taking any shots, put 3-4 patches of solvent (Butch's Bore Shine or Shooters Choice) down the barrel.
2.Let the last application soak 2 minutes.
3.Dry patch the barrel.
4.Wet-patch with Sweets copper solvent twice, being sure the entire barrel is wet. If the patch is too tight or not well soaked with Sweets you may miss moistening some spots in the barrel.
5.Let second application of Sweets soak 5 minutes.
6.Dry patch, noticing the blue streaks on the patch.
7.Fire a single shot.
8.Repeat steps 1-7 until the blue copper color on the patch is dramatically reduced. Your barrel is then broken in.
9.Once you have a clean patch, follow by putting a patch moistened with gun oil down the barrel. Seldom can you break in a barrel with fewer than 10 cleaning/firing cycles, but it should not take more than 25 unless you are working with larger calibers. Note: The use of brushes is fine in everyday cleaning, but not in the barrel break in process. If you use a brush, the copper reading will be coming from the brush rather than from the barrel itself.