Java 2D Game - MouseClicked & MouseMoved methods

Problem
I have two MouseEvent handlers (mouseClicked and mouseMoved), and they both work, but only separately.

If I click the mouse, the action gets processed fine. (bullet gets fired)
If I move the mouse, the action gets processed fine. (the sprite moves)

The problem occurs when I do both actions at the same time (moving mouse whilst clicking). The mouseMoved event goes through fine, but the mouseClicked event doesn't get called.

The below code is in my Game class constructor, which is extending JPanel.

    this.addMouseListener(new MouseAdapter(){
        @Override
        public void mouseClicked(MouseEvent e){
            //This creates a new bullet, and adds to an array to get drawn.
            bullet = new Bullet(105, e.getY()+5, bulletTexture);
            bulletsOnScreen.add(bullet);
            e.consume();    
        }
    });



    this.addMouseMotionListener(new MouseAdapter(){
        @Override
        public void mouseMoved(MouseEvent e){
            //This increments the sprites position on the screen.
            player.setYPosition(e.getY()-50); 
            e.consume();
        };
    });

What I've tried

I have tried using SwingWorker objects to run the mouseMoved in a background thread, but the results are the same (bullet doesn't fire).

        @Override
        public void mouseMoved(MouseEvent e){

            SwingWorker myWorker = new SwingWorker<Void, Void>(){

                @Override
                protected Void doInBackground() throws Exception {
                    player.setYPosition(e.getY()-50);
                    e.consume();

                    return null;
                }

            };

            myWorker.execute();
        };

I have also tried to check for a mouseClick within the mouseMoved method, again to no success.

        public void mouseMoved(MouseEvent e){
            if(e.getButton() == MouseEvent.MOUSE_CLICKED){
                //Create bullet and add to array (but this never gets called)
            }

            player.setYPosition(e.getY()-50); 
            e.consume();
        };

If anyone has any ideas or pointers, it would be great thanks.