My pencil (drawing program) is too slow!

Question

I have a "pencil" function similar to the one in paint() where I press the mouse and it draws on a JPanel.
However, pretty quickly it gets slow and the drawing can't keep up with the mouseDragged events. How can I make this faster?
this is my class representing the pencil drawingfunction:
import javax.swing.event.MouseInputListener;
import java.io.Serializable;
import java.awt.event.MouseEvent;
import java.awt.geom.Point2D;
import java.util.LinkedList;
import java.awt.Point;
import java.awt.Color;
import java.util.ListIterator;
import java.awt.Graphics2D;
public class MyFreeDraw implements MouseInputListener, ShapeObject, Serializable
        private LinkedList allPoints;
        private Color color;
        private Integer strokeSize;
        private String userName;
        private static final long serialVersionUID = 42L; //needed to reduce errors that can arise ina  weird way
     public MyFreeDraw()
            color = Color.BLACK;
            allPoints = new LinkedList();
            strokeSize = new Integer(1);
        public MyFreeDraw(Color color, int strokeSize, String userName)
            this.userName = userName;
            this.color = color;
            this.strokeSize = new Integer(strokeSize);
            allPoints = new LinkedList();
        public LinkedList getAllPoints()
            return allPoints;
        public int getSize()
            return allPoints.size();
        public Color getColor()
            return color;
        public int getStrokeSize()
            return strokeSize.intValue();
        public String getUserName()
            return userName;
     public void setColor(Color color)
            this.color = color;     
        public void setStrokeSize(int strokeSize)
            this.strokeSize = strokeSize;
        public void paint(Graphics2D g)
            g.setColor(color);
            g.setStroke(StrokeLibrary.getDrawingStrokeSize(strokeSize));
            LinkedList tempPoints = new LinkedList(allPoints); //avoids ConcurrentException
            if(allPoints.size()>=2)
                ListIterator it2 = tempPoints.listIterator(0);
                ListIterator it3 = tempPoints.listIterator(1); //must be one step ahead since two points are needed to draw
                while(it2.hasNext() && it3.hasNext())
                    Object ob2 = it2.next();
                    Object ob3 = it3.next();
                    if(ob2 instanceof Point)
                        Point p = (Point) ob2;
                        Point t = (Point) ob3;
                        g.drawLine(p.x, p.y, t.x, t.y);
        public boolean equals(Object other) //needed because otherwise the same object will be saved twice in the model!
            if(this == other)
                return true;
            else
                if(other instanceof MyFreeDraw)
                    MyFreeDraw test = (MyFreeDraw) other;
                    if(this.userName.equals(test.userName) && this.color.equals(test.getColor()) && this.strokeSize.equals(test.getStrokeSize())&& this.allPoints.equals(test.getAllPoints()))
                        return true;
                    else
                        return false;
                else
                    return false;
        public int hashCode() //not tested
            int ret;
            ret = userName.hashCode() +color.hashCode() + strokeSize.hashCode() +allPoints.hashCode();
            return ret;
     public void mousePressed(MouseEvent e)
            Point p = new Point(e.getPoint()); //Point p = new Point(e.getPoint());
            allPoints.add(p);     
     public void mouseDragged(MouseEvent e)
            Point p = new Point(e.getPoint());
            allPoints.add(p);
     public void mouseReleased(MouseEvent e)
            Point p = new Point(e.getPoint()); //Point p = new Point(e.getPoint());
            allPoints.add(p);
       public void mouseEntered(MouseEvent e) {};
       public void mouseMoved(MouseEvent e) {};
       public void mouseClicked(MouseEvent e) {};
       public void mouseExited(MouseEvent e) {};
}

Answer 1

Instead of storing every point the mouse has been, you can draw directly onto a BufferedImage from your mouseDragged() method. All you would need to do in your paintComponent() method is draw that BufferedImage.
public void mouseDragged(MouseEvent e)
   Graphics g = image.getGraphics();
   g.drawLine(lastX, lastY, currentX, currentY);
}