Using a bluetooth keyboard with multiple devices

I was able to pair my Apple Bluetooth keyboard with my MacBook Pro and my iPad.

I usually use it with my Mac. But when I just need to do emails then I just turn on bluetooth on my iPad and after a few seconds it connects to the Bluetooth keyboard and is ready to use. I don't have to un-pair or anything. It just works.

When I am finished with my iPad then I just disable bluetooth so there are never two bluetooth devices trying to connect to the keyboard at the same time.

However, I have problems connecting my iPhone 4 to the keyboard. When I go to settings and enable bluetooth then it doesn't show the Bluetooth Keyboard at all! How can I fix that?