In Disk Utility, does Secure Erase include the Erase Free Space option
Secure Erase supersedes Erase Free Space because it zaps the entire disk instead of just zapping a subset of the disk marked 'free space.' If you want to be sure the NSA can't read this disk, do the Most Secure 7-pass erasure.

BTW: The 7-pass job takes lots of time (many hours to days) and gives the disk a good thrashing, too. Its a good stress test.