This is a Houser brand French horn mouthpiece. I am selling it because I no longer use it. There is no rim. It should fit rims from American manufacturers like Giardinelli. The bore size is 10, and the cup is moderately deep, not too deep. It's made of stainless steel, so it responds well and makes high notes easier to hit. It has some signs of use, but it doesn't affect the playing at all. Please be aware that there are some signs of use before purchasing. Please check the Houser website for details about the mouthpiece. No claims, no returns.