[...]

   Ramon> How can I reduce those images to a more reasonable size?
   Ramon> Is the some sort of built-in switch (in ImageIO or in the
   Ramon> full JAI) to specify the desired DPIs of the displayed
   Ramon> image?

   Ramon> Or will I have to resort to some transformation

One way is to use the standard Java2D transforms. Something like the
following assuming we are drawing into a JComponent

   protected void paintComponent(Graphics g)
   {
       super.paintComponent(g);

       Graphics2D g2 = (Graphics2D) g.create();

       AffineTransform transform = new AffineTransform();

       // Translate so we don't draw in the component's borders
       Insets insets = getInsets();
       transform.translate(insets.left, insets.top);

       // Scale accessors return doubles indicating scale factor
       // on each axis
       transform.scale(getXScale(), getYScale());

       g2.transform(transform);

       // Accessor returns the image created from the TIFF file
       Image image = getImage();
       if (null != image)
       {
           g2.drawImage(image, 0, 0, this);
       }

       // As we created a new Graphics2D above we must free
       // any system resources
       g2.dispose();
   }

I guess in your case you won't want a different scale on each axis,
otherwise the aspect ratio of the image will change.

What I do in our application is allow the user to control the scale
interactively with a JSlider so that they can make the image a size
which is comfortable to view.