This was copied from Badger Barrels website. They make custom barrels for competitve shooters. The first section is directed towards smokeless/CF barrels but i thought i would include it anyway. Scroll to the bottom for black powder.
BREAK-IN PROCEDURE FOR BARRELS-Jacked bullets
For the first ten shots we recommend, if possible, using jacketed bullets with a nitro powder load. Clean the oil out of the barrel before each shot using something as simple as Windex which will soak the oil out of the pores. After firing each bullet use a good copper cleaner (one with ammonia) to remove the copper fouling from the barrel. We do not recommend anything with an abrasive in it since you are trying to seal the barrel, not keep it agitated.
After cleaning with bore cleaner, clean with Windex after each shot. Use Windex because many bore cleaner use a petroleum base which you want to remove before firing the next shot. This will keep the carbon from building up in the barrel (oil left in the pores, when burned, turns to carbon).
To keep the temperature cool in the barrel, wait at least 5 minutes between break-in shots. The barrel must remain cool during the break-in procedure. If the barrel is allowed to heat up during the break-in, it will destroy the steel's ability to develop a home registration point, or memory. It will have a tendency to make the barrel "walk" when it heats up in the future. I am sure we all have seen barrels that, as they heat up, start to shoot high and then "walk" to the right. This was caused by improperly breaking in the barrel (generally by sitting at a bench rest and shooting 20 rounds in 5 minutes or so). Then, for the rest of the guns life the man complains that barrel is no good. If you take a little time in the beginning and do it right, you will be much more pleased with the barrel in the future.
If you look into the end of the barrel after firing a shot, you will see a light copper-colored wash in the barrel. Remove this before firing the next shot. Somewhere in the procedure, around shot 6 or 7, it will be obvious that the copper color is no longer appearing in the barrel. Continue applications through shot 10.
If you have any ammunitions left, you then may shoot 2 rounds and clean it for the next 10 shots. this is simply insuring that the burnishing process has been completed.
IN theory you are closing the pores of the barrel metal which have been opened and exposed through the cutting and hand lapping procedures.
BREAK-IN PROCEDURE FOR BARRELS-Lead bullets
The same shooting-cleaning process may be used when firing lead bullets and black powder with this exception: shoot 2 bullets, then clean for the first 30 rounds. Naturally, you will use a cleaner appropriate for black powder. You can also use harder lead if available to accelerate the break in. This will accomplish the same as the jacketed bullets.
It may take 80 to 100 rounds to break in with lead. That is why we recommend using jacketed bullets when possible. After this procedure, your barrel's interior surface will be sealed and should shoot cleaner and develop less fouling for the rest of its shooting life.
