TComboBox: Displaying Hint Hovering Over Dropped-Down List

Delphi 4
Windows NT 4 SP4

I have a TComboBox that contains a list of file paths.  Naturally, these are
usually longer than the width of the box.  I can use the Hint property to
display the file path that is in the main text part of the box, but I would
like to be able to display any path in the dropped-down list when hovering
over that path.

Can anyone provide the technique or an example of doing this?

Regards --

Philip Brooke