I've taken to using JB Bore Compound in place of conventional break-in procedures. I first got the idea reading Varmint Al's site. He cleans the bore and gets out the JB and gets about 50 full strokes in with it and calls it done. He described one gun in which that proved inadequate and he went to a second treatment with Flitz.
The way I do it is more aggressive. I've firelapped enough bores now to have lost my fear of the judicious use of a bit of abrasive in a bore. I fire just one shot, use Boretech Eliminator to remove fouling and copper (I used to use Sweet's 7.62, then Butches Bore Shine — any copper removing bore solvent will work — but Eliminator is faster, odorless and non-toxic and has enough water to handle accidental use of corrosive primers). After there is no copper left, then I apply the JB. I always do this working from the breech end with a bore guide in place to keep the chamber minimally dirtied. I run the patch in and go back and forth in short strokes while inching the patch down the barrel. By the time it gets to the muzzle I've got 20 or 30 short strokes in and usually add a long stroke or two. The idea is the abrasive is most fresh near the breech where the most fouling is normally left.
After doing that for 20 rounds, you should notice the barrel cleans more easily. It won't clean the way a firelapped barrel does (that's a dramatic difference) but it should be about as good as commercial barrels get without lapping. I no longer mess with the break-in procedures that have you simply clean with a solvent and brush between each round, then, after 20 or so, clean every three, then later every five rounds and so on. They can use up 100 rounds and, in really rough bores, often don't seem to make a whit of difference. My first Garand's barrel was like that. The JB will positively smooth the surface and dull sharp edges that grab copper. If it fails to make the gun as easy to clean as you think you want it, then you need to look at firelapping. Hand lapping involves more work and skill, but if you are good at it, it will make the bore very uniform.
Incidentally, when I got tired of watching the Garands accuracy drop off during the slow fire stage of the National Match Course (between rounds 30 and 50), then taking all night with Sweet's to clean out, I finally did buy a NECO kit and firelap it. Based on measuring the number of patches required to complete cleaning, the improvement was about 6:1. No more accuracy loss even during an 80 round + sighters NRA Service Rifle match.