there is a ceiling system that the grid attaches directly to the floor joists. Most folks I have talked to do not like it.
other than that, the lights used is usually the determining factor as to how much room you need. The less room you have, the harder it is to install and/or remove the tiles but I have had carpenters build my light in place because the space was so shallow, I could not install as usual.
It depends on wires, pipes, lights and anything else in the way. Generally a 3 inch drop is minimum for getting tiles in and that is tight. Ceiling max is the grid that is installed tight to the joist and is sold at home depot. It isn't the easiest to work with but it is a decent product once you figure it out.