Krieger recommends a shorter break-in than most with stainless barrels, and about 3-4x that much for chrome-moly. They also mention that the first few shots, which smooth out microscopic burs in the throats from chambering, will copper foul A LOT, and that if too many shots are fired, this copper can me difficult to remove. My take on it is simply this - if you shoot too many shots before cleaning a new barrel, you will have to make more passes to get the copper out than if you only took a shot or two, and it may take 40 shots to break-in instead of 20 because that copper build-up protects the burs from being removed by subsequent shots. I do not believe break-in to be highly critical.
On a related, but slightly side note, I've found multiple shooters recommend that spend 75-100 rounds practicing with a new barrel before doing load development, because when they chrono a new barrel, the chrono shows the barrel to be getting faster as it gets shot more for about the first 75-100 shots. The result is that if you find a good load during that time, your load will end up shooting faster, and you'll have to load down to get back on that node again. On top of that, they mention that pressure signs decrease over the same time period, so now you can actually load more powder than your max load showed to be early on. The point was, wait until the rifle settles in before doing load developement. If you don't want to "waste" shots with a break-in procedure, then just load up some ammo, sight-in, and do some practice. When you're done, and cleaning the copper out seems to take an awful long time for a "superior hand lapped barrel" just realize that it will be much better after the first few trips.
I just "broke-in" a brand new Krieger using their prescribed method, except that I always shoot WS2 coated bullets. I never got copper to show up on a single patch using Bore Tech Eliminator, and if you've ever used that stuff, you know it should be turning patches blue.
