The Moment case, which just entered a Kickstarter, is designed to work in conjunction with Moment lenses. Since they're all-metal and need a specific mount material that's not terribly friendly as a stick-on mount, this is a better solution.
Without the lens, the case is relatively thin, though it gets a little bulky at the grip area. The grip contains a battery to power the sensor and the shutter connection; it takes a standard coin cell battery. The case will have a magnetized lens cap that can be attached to the body when not in use.
The shutter button is in a traditional location on the right side of the grip. When holding the case, it felt like an alternative shutter on the left side might make it more suited when operating the screen with your right hand.