Dumb trait got to me...need help getting my head around a mod. (Zyraniator + Double Barrel)

So I have the Zyraniator pistol, and I love it. Current damage is 37 (x3), presumably because it fires in three shot bursts. Uses three bullets per, etc.

I have the Double Barrel mod, which "doubles the number of shots fired at the expense of reduced Damage and Damage-type side-effects." On the surface I understand why this should be *better*; each bullet is now two bullets that combined do more damage than the one bullet originally did.

I use this mod, and the stats for the gun become 21 (x2). Seemingly much worse. But I pull the trigger and a.) it appears to still fire three shots and b.) still uses three bullets.

Now, here's the thing: it *feels* like it does more damage **with** the mod. But I can't figure out why that would be true. Part of it is that I'm not sure I'm reading the damage numbers correctly; I'd assumed 37 (x3) just meant 37 damage per bullet in a three-shot burst, for total damage of 111. But 21 (x2) still seems like a three-shot burst, and I can't really figure out where the "doubles the number of shots fired" effect comes in.

At the end of the day, it feels like I'm just imagining that it's better with the mod, and that perhaps this is not the right kind of gun for this mod.