Yep. You write them you own them. Post it somewhere that date stamps it,e.g. SoundCloud and don't worry unless it's lawsuit time at which point you can copyright them. Some folks mail the song to themselves and don't open the package.
The only thing that will stand up in court is a copyright from the government. Don't wait until you want to sue as the other party may have copyrighted it themselves and then you are SOL.