If you booked an Early Saver fare the price can be adjusted even if you paid in full. I made 3 Early Saver requests after being paid in full. My Travel Agent was causing me some problems because every time I adjusted down they lost part of the commission and had to do extra paperwork. Life is hard that way. If my travel agent didn't want to deal with early saver they shouldn't have let me book that way. They gave up the reservation to Carnival in case I had more early saver requests.
If you booked with a travel agent that agent has to put in the early saver request. Here is a link to Carnival's website about the early saver program.
Frequently Asked Questions
I did get the price drops in the form of On Board Credit (OBC), since carnival charges $10 per day per person for tips I don't mind the OBC.