Double encrypted backup?

My MBP (Mavericks) drive is encrypted with Filevault 2, and my external backup drive is also encrypted using Disk Utility as OS X Entended (Jounaled,Encrypted). When I set up Time Machine to back up to the external encrypted drive, I chose the encrypted backup option. Are my backup files now encrypted twice? I'm unclear on where the external drive encryption is taking place vs the Time Machine encryption.

Thanks.

MBP mid-2010, 8GB DDR3, 500GB internal, OS X 10.9.2, 1 TB LaCie Rugged external backup.