The way I understand it, what we're doing when using one of the many variations of the Sinclair method of breaking in a barrel could more properly be called burnishing the bore.
The shoot once, clean, X5; then shoot 3 times, clean, for the next 15 rounds, and then after every fifth round, for another 25 rounds, is a short description of the "Sinclair method". The cleaning regimen is 1 wet patch, then 1 dry patch, then 1 wet patch, followed by 1 fore-and-aft stroke with a wet bronze bore brush for each round fired depending where you are in the process, then 1 wet and 2 dry patches. The bronze brush is cleaned after every 1,3, or 5 complete passes, with aerosol solvent. I use 'Lectra- Motive which is similar to brake cleaner you can buy at an Auto parts store.
The wetting agent (solvent) used is a special witches' brew. The recipe I use is equal parts shooter's choice copper solvent, Kroil, and GM top cylinder lube. You can get the top cylinder lube from any GM dealership's parts counter.
This solvent mix is potent and effective. Use outdoors and be upwind.
The break-in process is best done in one session so that the heating up of the barrel from shooting helps the solvent work.
You need to use a tight-fitting patch on a pierce-type jag, so that you do not pull the patch back through the bore. I like to catch my patches in an empty plastic pop bottle that I slip over the muzzle(you go through a lot of patches doing this). Use good quality cotton patches; I like the ones from shooter's choice. Use the right size for your bore too.
Some guys will comment that it seems foolish to use strong copper solvents with a bronze bore brush. The object of this method is not to "polish out" machine marks. The Sinclair method of break-in both smooths out any burrs, sort of knocks off the high spots(very tiny ones) and fills in any micro-pores or cracks in the bore metal with jacket material, the goal being a surface that's smoother than what was provided in the factory production barrel.
The lapping process described in the stickies at the top of this forum, is a quick and effective way to smooth out the imperfections left by the factory production process.
Both should improve a roughly finished bore. I've had brand-new rifle barrels, and not just from NEF, that had rough spots that felt like my patch was riding on thousands of tiny burrs as if the bore had steel hairs sticking up out of the surface of the lands /grooves. I had a Ruger 220 Swift that absolutely would not shoot; the last 2 inches of the bore up to the muzzle was rough as a cob. You could see pieces of patch material stuck to the inside of it. I had the last 2 inches of this barrel cut off and cut in half the long way so I could examine it closely--It is full of tiny holes called inclusions that are the result of a bad batch of steel getting past quality control at both the mill and the ruger barrel makers.
A custom, high-end benchrest-quality barrel should come from the barrelmaker's shop with a much smoother, uniform interior surface than any production rifle. The lands of such barrels are sharp and the surfaces are smooth; aggressive break-in procedures like the one I've described can shorten the competitive life of such a barrel; certainly the lapping process described in the stickies is not for those types of tubes. When you pass a tight-fitting patch through a Lilja or a Shilen match-grade barrel, it should feel like it's riding on snot-covered glass.
EDIT:
Darn!!
I type for 20 minutes and post, only to find a link that says it all in about 1/3 the wordage!!
You're the best, Tim!!