Thank you, but that wasn't really what I was trying to get at.  None
of the containers described in that quote are JComponents.

I don't want the entire JApplet to use a layered pane.  I want a
subsection, added to a JPanel, to be layered.

The tutorial you linked, which I have read (but possibly not in enough
detail), has example code that uses JFrame's setContentPane() method to
use a custom built JLayeredPane.  I want to know if I can do something
like:

JPanel panel = new JPanel();
JLayeredPane layers = new JLayeredPane();

// add stuff to JLayeredPane

panel.add(layers);

So far, it hasn't worked: the area that should contain the layers is
just grey/blank.

Here's some example code; the actual app for which I'd like this
functionality is pretty complicated.  But I think if I could get this
sample to work, I could also get the app to work:

import javax.swing.JFrame;
import javax.swing.JLabel;
import javax.swing.JLayeredPane;

  public class LayeredPaneTest
  {

     public static void main (String[] args)
     {
        go();
           
        protected static void go()
        {
           JFrame frame = new JFrame();
           JLayeredPane pane = new JLayeredPane();
           pane.add(new JLabel("foo"), new Integer(0));
           pane.add(new JLabel("bar"), new Integer(1));
                   
           frame.getContentPane().add(pane);
           frame.pack();
           frame.setVisible(true);
        }
           
     }
  }