To install a Cutts Compensator, the barrel is shortened and the base unit soldered on the end, so it's pretty much a permanent installation. IMHO, only a damaged barrel could justify its removal for installation on another barrel.
The Cutts served three purposes: It acted as a muzzle brake to reduce recoil and muzzle rise (the Cutts is seen on many Thompson sub-machine guns); it controlled the shot pattern by reducing pellet deformation in the choke transition area (this was in the pre-plastic shot cup days), and it allowed screw-in choke changes. However, with the Cutts it was actually a "screw-over" configuration. It avoided the thin wall work required for machining modern screw-in choke tubes.
The Cutts is also responsible for the reputation of muzzle brakes being too noisy. It's not that they are any noisier, they just redirect the sound. So, if you shoot with a Cutts you may not be extra popular in a crowded duck blind or a shoulder-to-shoulder buddy shoot.
In its day, the Cutts and the Simmons rib were very popular on Model-12. The Cutts was also seen on many Browning Auto-5s / Remington 11s. Westfi1, if you don't want the Cutts on your Model-12, don't remove it, get a new barrel.
[SIZE=-2]photo: United States Guns & Arms Collectors[/SIZE]