BufferedImage Combining images

Question

I am working with the BufferedImage class. Basically I have two images
that I want to combine together BEFORE I paint them to the screen. Can someone please show me how to do this. I have not been able to figure this out, although I think it will be easy for a seasoned Java Graphics developer.
1 Image FirstImage = getToolkit().getImage("front.gif");
2 Image MyButtonImage = getToolkit().getImage("buttons.gif");
3 MediaTracker mt = new MediaTracker(this);
4 mt.addImage(FirstImage, 1); mt.addImage(MyButtonImage, 2);
5 bi_BackGround = new BufferedImage(FirstImage.getWidth(this),
6 FirstImage.getHeight(this),
7 BufferedImage.TYPE_INT_ARGB);
8 bi_MyButtonImage = new BufferedImage(MyButtonImage.getWidth(this),
9 MyButtonImage.getHeight(this),
10 BufferedImage.TYPE_INT_ARGB);
11
12 Graphics2D dcBackGround = bi_BackGround.createGraphics();
13 Graphics2D dcButton = bi_MyButtonImage.createGraphics();
14
15
16 dcBackGround.drawImage(FirstImage, 0,0, null);
17 dcBackGround.drawOval(10,10,5,5); // Draw an oval on the first image
18 // I am under the assumption that lines 16, and 17
19 dcButton.drawImage(FirstImage, 0,0, null);
// Next draw image of a button on the first image.
20 dcButton.drawImage(MyButtonImage, 0,0, null);
21 // We now have a background image with a button on it.
22 }
23
24 public void paintComponent(Graphics g) {
25 super.paintComponent(g);
26 Graphics2D g2D = (Graphics2D) g;
27 g2D.drawImage(bi_MyButtonImage, x, y, this); // Display final image
28}

Answer 1

Actually the code could be working but I have just found out that
only a portion of the first image is being shown. Then I think the second image is overlayed with the same dimensions of the first image, thus hiding the second image. For some reason, the hieght of the bitmap is not correct. Note that this is how I get the height.
FirstImage.getWidth(this),
FirstImage.getHeight(this)
Please help