How to create a JButton with a menu?

Above, Adam Goode asked,

Does your solution have the behavior where if you click the button again with the menu up, it pops up the menu again, instead of dismissing it?

This turned out to be a testing task. I finally solved it with an invokeLater to re-vanish the popup in that particular case. My solution also allows the client to tailor the button and the popup menu.

    /**
 * A button that will popup a menu.
 * The button itself is a JLabel and can be adjusted with all
 * label attributes. The popup menu is returned by getPopup;
 * menu items must be added to it.
 * <p>
 * Clicks outside the menu will dismiss it.
*/
public class MenuButton extends JLabel 
        implements MouseListener, PopupMenuListener {
    JPopupMenu popMenu;

    @SuppressWarnings("")
    public MenuButton() {
        super();
        popMenu = new JPopupMenu();
        addMouseListener(this);
        popMenu.addPopupMenuListener(this);
    }

    public JPopupMenu getPopup() { return popMenu; }
    
    @Override
    public void mousePressed(MouseEvent e) {
        if ( ! popMenu.isShowing()) {
            popMenu.show(this, 0, getBounds().height);
        }
    }
    @Override public void popupMenuWillBecomeInvisible(PopupMenuEvent e) { 
        SwingUtilities.invokeLater(()->{
            if (popMenu.isShowing()) {
                //  if shpwing, it was hidden and reshown
                //  by a mouse down in the 'this' button
                popMenu.setVisible(false);
            }
        });
    }

    @Override public void mouseClicked(MouseEvent e) { }
    @Override public void mouseReleased(MouseEvent e) { }
    @Override public void mouseEntered(MouseEvent e) { }
    @Override public void mouseExited(MouseEvent e) { }
    @Override public void popupMenuWillBecomeVisible(PopupMenuEvent e) { }
    @Override public void popupMenuCanceled(PopupMenuEvent e) { }

} // end MenuButton

Sample invocation

    MenuButton button = new MenuButton();
    JPopupMenu menu = button.getPopup();
    menu.add("Browse Sample");
    menu.add("Save As ...");
    Icon hamburger = IOUtils.loadIconResource(
            IndexGofer.class, "images/hamburgerMenu.png");
            (IOUtils is on page http://physpics.com/Java/tools/
                  You should use your own tool to load an icon.)
    button.setIcon(hamburger);
    button.setOpaque(false);