Can I just add, this is the way I did it...
In order to get unrestricted FAA CPL, you need to do 10 hours night flying, now, if your JAA PPL does not have night flying, then you need to do this before you convert your JAA to FAA (you can do this in the states), else, you will find that your CPL (if you can get it) will have a night restriction.
Speak to the school you will be flying at about it.