mouse-over popup menus

A GUI designer has asked us to make a JPopupMenu
where the menu items become visible when the mouse
goes over them, instead of when they are clicked.
It works pretty well with a MouseAdapter that overrides
mouseEntered() and sets the menu's getPopup() to visible.

There's a problem though. When the user wants to get
rid of the popup, in a normal JMenu they can click somewhere
outside the menu and the current popup disappears.
But with the popup that has become visible with mouse-over
it is always staying visible.

Does anybody know how this works in a standard JMenu?
I've been reading the sources but so far haven't found it.
Thanks. Source for running example below:

import java.awt.*;
import java.awt.event.*;
import javax.swing.*;

public class Menus extends JFrame {

    public Menus() {
        super("Menus");

        String [][] items = {
          { "Save" },
          { "File" , "Open", "Save As", },
          { "Edit", "Cut", "Copy", "Paste", "A long looooooooooooooong
item", },
          { "View", "Full screen", }
        };

        JMenuBar menuBar;
        JMenu menu, submenu;
        JMenuItem menuItem;

        menuBar = new JMenuBar();
        setJMenuBar(menuBar);

        for (int i=0; i<items.length; i++) {
            menu = new JMenu(items[i][0]);
            menu.addMouseListener(new MouseL(menu));
            menuBar.add(menu);
            for (int j=1; j<items[i].length; j++) {
                menuItem = new JMenuItem(items[i][j]);
                menu.add(menuItem);
            }
        }

    }

    private static class MouseL extends MouseAdapter {
        private final JMenu _menu;
        private static JPopupMenu currentPopup = null;

        MouseL(JMenu menu) {
            _menu = menu;
        }

        public void mouseEntered(MouseEvent e) {
            if (currentPopup != null) {
                currentPopup.setVisible(false);
            }
            Point menuLoc = _menu.getLocation();
            Dimension menuSiz = _menu.getPreferredSize();
            // System.out.println("loc=" + menuLoc + ", siz=" +
menuSiz);
            JPopupMenu popup = _menu.getPopupMenu();
            popup.show(_menu, 0, menuSiz.height);
            currentPopup = popup;
        }
    }

    public static void main(String[] args) {
        Menus frame = new Menus();
        frame.setSize(new Dimension(400, 200));
        frame.addWindowListener(new WindowAdapter() {
            public void windowClosing(WindowEvent e) {
                System.exit(0);
            }
        });
        frame.setVisible(true);
    }
}