InvokeLater does not update in time

Hi everybody,

I'm working on a small application that scans a lot of files for
information.

To let the user know what is going on, I update the following components:
- a JList containing log messages
- a JProgressBar indicating the progress in the current file
- a JProgressBar indicating global progress

The scan progress is a separate thread. I noticed that the JList was not
getting updated correctly, and after some Googling I found out that this
was because I was not updating it in the Event Dispatching Thread. So I
added the following piece of code:

--- code ---
    if (SwingUtilities.isEventDispatchThread())
    {
        sv.showMessage(message);
    }
    else
    {
        Runnable run = new Runnable()
        {
            public void run()
            {
                sv.showMessage(message);
            }
        };
        SwingUtilities.invokeLater(run);
    }
--- /code ---

"sv" is the JFrame containing the JList. This would ensure that a) the
JList would get updated, and b) that the results would be displayed in
the EDT.

So far so good - but as a result of the amount of files, there will be
thousands and thousands of Runnables, each waiting their turn to get
executed.

The end result is a display in which both JProgressBars are both at 100%,
and the JList still is updating a list of what's going on.

How can I let the update process for the JList keep pace with the
JProgressBars?

Thanks in advance,

Ikke