A game controller includes a grip, one or more finger-actuatable controls on the grip, and a rim located on the grip. The rim defines an aperture. The game controller further includes a paddle-actuatable sensor accessible through the aperture and a pivot spaced apart from the aperture. The pivot is configured to removably affix a selected paddle accessory to the game controller and to translate a touch applied to the selected paddle accessory outside of the aperture to an actuation of the paddle-actuatable sensor inside the aperture.