WindowUtils.setWindowTransparent(Window w, boolean transparent);
This effectively gives the window a transparent background. The alpha levels of the window's contents are preserved.
The demo is similar to the previous one but adds a few standard components to the mix.
UPDATE If you have a linux system and this for some reason doesn't work, please post a comment to that effect, or post a message to email@example.com so we can ensure this works reliably across all linux systems (64-bit is in the works).