Adding fixed position content to a scrolled panel

I have a problem with a drawn panel which is embedded into a
JScrollPane. Most of the content needs to scroll with the pane, but I'd
also like to be able to add a small label at a fixed position in the
viewport.

It seems like I should be able to do this using the getVisibleRect()
function to see what we're looking at and moving the position of the
fixed component to compensate.

However when I do this I get odd effects. If I scroll by clicking on
the empty parts of the scroll bar everything works fine, but if I drag
the scrollbar handle or use the arrows at the end the fixed text scrolls
with the window, leaving a ghost trail behind it. I'm assuming this is
an optimisation the ScrollPane makes, but I've looked and can't find how
  to turn it off.

I've attached a short program which demonstrates this. Any suggestions
for how to get this working would be most appreciated.

Cheers

Simon.

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

public class ScrollBug extends JFrame {

    private JScrollPane scrollPane;

    public static void main(String[] args) {
        new ScrollBug();
    }

    public ScrollBug () {
        scrollPane = new JScrollPane(new BigPanel());
        setContentPane(scrollPane);
        setSize(500,100);
        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        setVisible(true);
    }

    private class BigPanel extends JPanel {

        public Dimension getPreferredSize () {
            return new Dimension(10000,100);
        }

        public void paintComponent (Graphics g) {
            super.paintComponent(g);
            Rectangle r = getVisibleRect();
            int x = r.x;

            for (int i=1;i<100;i++) {
                g.drawString("Moves "+i, i*100, 40);
            }
            g.drawString("Fixed Position", x, 20);
        }
    }
}