How to select first item in JPopupMenu?

Question

In the past, when one made a JPopupMenu visible it's first item would get selected by default: http://weblogs.java.net/blog/alexfromsun/archive/2008/02/jtrayicon_updat.html

Nowadays the default behavior is to pop up the menu without any item selected. I would like create a JPopupMenu with a single item that will pop up selected and centered under the mouse pointer. I have managed to get the item to pop up centered under the mouse but I the JMenuItem refuses to render as if it is selected. If I move the mouse out of the item and back in it selects properly.

Any ideas?

Here is my testcase:

import java.awt.Component;
import java.awt.Point;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.awt.event.MouseAdapter;
import java.awt.event.MouseEvent;
import javax.swing.JFrame;
import javax.swing.JMenuItem;
import javax.swing.JPopupMenu;

public class Test extends JFrame
{
    public static void main(String[] args)
    {
        JFrame frame = new JFrame();
        frame.setSize(800, 600);
        frame.getContentPane().addMouseListener(new MouseAdapter()
        {
            @Override
            public void mousePressed(MouseEvent e)
            {
                if (e.isPopupTrigger())
                    popupTriggered(e);
            }

            @Override
            public void mouseReleased(MouseEvent e)
            {
                if (e.isPopupTrigger())
                    popupTriggered(e);
            }

            private void popupTriggered(MouseEvent e)
            {
                JPopupMenu menu = new JPopupMenu();
                final JMenuItem item = new JMenuItem("This is a JMenuItem");
                menu.add(item);
                Point point = e.getPoint();
                int x = point.x - (item.getPreferredSize().width / 2);
                int y = point.y - (item.getPreferredSize().height / 2);
                menu.show((Component) e.getSource(), x, y);
            }
        });
        frame.setDefaultCloseOperation(JFrame.DISPOSE_ON_CLOSE);
        frame.setVisible(true);
    }
}