Removing all instances of "NOT NULL" from an entire directory of files

OK, I've got a command (or two) that will remove all NOT NULL strings from a
given file.

cat filename | perl -pi -e "s/NOT NULL//g" > filename

But how do I run that command on every file in a directory, successively?

(In case you're wondering, I'm working on the pgsql/ directory of .sql files
that interchange uses to build the database tables).

Thanks,

Dan Browning
Network & Database Administrator
Cyclone Computer Systems