Oh, yeah, the whole roommate thing is probably another posting in itself. The more I think about it, and I have also asked a couple of friends in construction, I don't know if there really is much you can do. Weighing mine down so that it doesn't bounce and move around helps a lot. But I had to fill it with sand and stack sandbags behind it. But with the actual punches, I honestly cant think of anything that would muffle the noise. Sorry.