I swear by JB and use for breaking in all of my new rifles. What really sold me on it was when I tried it on my .303 Enfield. Shot groups went from 3+ inches at 100 yards to 1" at 100 yards, and the only the thing I did was clean the barrel with JB. It made a big difference on my mini as well.
I use a wire cleaning brush and wrap a patch around the wire brush. Then dip in JB and make 10 strokes. Finish off with Hoppes #9 and then a dry patch. I generally use it every 300 rounds or so, but more often with the mini for now. The barrel just isn't quite there yet. I've noticed when a barrel is right that a semi loose patch at just the right speed will whistle when it goes down the barrel. Mine is not quite to that point.