Some people asked me about the Visible-/ Invisible-List of ICQ. But I thinks it's very easy:
If you put somebody on your Visible-List, the user can see you always. It doesn't care if you're on-line or invisible.
If you put somebody on your Invisible-List, the user can't see you anymore. There's no difference if you're on-line or invisible, he can't see you.
At last, if you put your status on invisible, only your Visible-List is able to see you on-line.