You can’t jailbreak iPod touch 3.1.3 untethered, but you can jailbreak iPod touch 3.1.3. iPod touch users will need to jailbreak again because Apple released the iPhone 3.1.3 update which updates the firmware and removes the jailbreak for current jailbroken iPod touch and iPhone users.
The jailbreak iPhone 3.1.3 post may help iPhone users.
