Should swing event handlers be queued after the event on the EDT?

Question

Should swing event handling code be queued after the event on the EDT? If so, is it the responsibility of the event source to schedule the event handlers, or is it the responsibility of the event handler to schedule the actual handling code later?

Consider:

JButton b = new JButton();
b.addActionListener(new ActionListener(){
    public void actionPerformed(ActionEvent e){
        /*
         * SNIP 1
         * do something that may affect other
         * components or generate new events...
         */

        // SNIP 2
        EventQueue.invokeLater(new Runnable(){
            public void run(){
                /*
                 * do something that may affect other
                 * components or generate new events...
                 */
            }
        });
    }
});

SNIP 1 runs handler code when the event is received. If the JButton takes responsibility for scheduling event by EventQueue.invokeLater(), then this is probably correct. SNIP 2 receives the event, and takes responsibility of scheduling handler code after the event is received (and handled by all other listeners for this specific event type). Which is correct?

EDIT: Just for clarity, I want to schedule event handlers later on EDT because changing state in the first event handler may hide original state at the time of the event from other event handlers for the component.