Shoot Through Walls
The bullets in MW3 multiplayer can, to a greater or lesser extent, penetrate walls, doors and the like. In other words, there is no reason to refrain from firing some rounds, even if a wall or a door separates you and your opponent.
You will probably have to shoot more rounds than usual to kill the character, if he’s standing behind a door. Yet, the result is the same in the end. You win.