Some say that the tension of the barrel band can influence accuracy. I've seen it written by many that the band should just fit snugly but not with any tension on the barrel. The tension can be relieved by sanding or polishing the inside of the band until it fits to suit you and the rifle.
There is quite a bit of informaiton on this posted in various places. Search Marlinowners.com, I'm pretty sure that noted lever gun smith Mic McPherson has also written about this as an enhancement to accuracy. You might also search Leverguns.com for further.