A swamped barrel is a barrel that tapers from both the muzzle and breech toward the middle of the barrel. It makes for a lighter, and more nicely balanced, rifle. It also looks neat when done well.
it does make for a good look, but most importantly, weight reduction and excellent handling of a long barreled rifle. For the past 2 years, a builder makes a gun and gives it away in a raffle at the local rendezvous.