database restore -- oops

OK, so I figured out one mistake.  Backing up the entire database in one system and restoring it in another is a bad idea.  It clobbers tables that plesk uses (for example to track certificates) and after that your system is doomed.  Also, I though that using mysql -u user -ppassword dbname < fullbackup.sql would only take the stuff that pertained to dbname -- no such luck.  It restored everything (which is certainly not what I wanted).  I need to find a way to reduce the .sql file to just the one database before doing the restore (or restore from backups of the dbs done one at a time.