Java Swing Tree with Streaming Updates

I have a Swing tree that is changing as a result of a background thread that receives updates to the tree, in a streaming fashion. Updates can come quite fast and they can be complex. And they can come fast enough that previous updates have not yet been rendered. I would like the tree displayed in the GUI to be visually updated, as fast as practical, as the tree model updates are applied.

Currently I have code abstractly as below:

public void ReceiveStreamDocument(final Document d) {
    SwingUtilities.invokeLater(new Ruable(){
        public void run(){
            ComplexChangeToTree(d);
            TreeReload();
        }
    });
}

Now the complex change is time consuming, what I would like is:

public void ReceiveStreamDocument(final Document d) {
    ComplexChangeToTree(d);
    SwingUtilities.invokeLater(new Ruable(){
        public void run(){
            TreeReload();
        }
    });
}

However the problem appears to be that modifications to the tree structure are now outside of the swing thread and when the tree is actually re-rendered there can be exceptions thrown. It does not seem to help to have something like this:

public void ReceiveStreamDocument(final Document d) {
    synchronized(root){
        ComplexChangeToTree(d);
    }
    SwingUtilities.invokeLater(new Ruable(){
        public void run(){
            synchronized(root){
               TreeReload();
            }
        }
    });
}

The TreeReload() is not actually updating the display, but rather just signaling that the display should be updated. I believe I need to override a painting operation somewhere and synchronize root on that, but I'm not sure where, or how, or indeed what is the best practice.