Yes, you got it.  This is will terminate the running instance that was opened by brackets irregardless of what  has been opened.  If i can somehow retrieve the URL of the window/tab you'd like to close, it would be possible to do what you want.  Otherwise, I won't be able to tell which is the right one to close (if there are multiple windows/tabs opened).  

On another tough useful note, perhaps the CloseLiveBrowser should have an "argURL" argument that is passed in.  This would not only make it consistent with the OpenLiveBrowser method call, but also make it easier to narrow down & target.  Other platforms are free to ignore this argument until their implementations are required to use it.

In any case, in lieu of a handy URL being passed in to the close call, do you know how I can retrieve it for comparison purposes?