Though it seems an oxymoron at first, this effect is quite frequently achieved by people at the very peak of high drama who wish to convey immense anger by leaving the room in a huff, but who don't want to wake the neighbors. A good quiet door slamming involves four steps.

1. Strut swiftly to the door
2. Shoot a withering glance over your shoulder at the offending party
3. Yank the door open hard and walk through it
4. Pull the door quickly shut until it is a few inches from closing, then abruptly stop, and quietly shut it the remaining few inches.