The site iJailbreak proposes software that permits running Jailbreak on the iPod Touch with firmware 1.1.3
It is necessary to start with an iPod Touch running firmware 1.1.1 or 1.1.2 and that already has Jailbreak installed. Apple will appreciate the fact that this activates software that normally one should pay Apple $20 for. It appears that these applications are already installed by default with firmware 1.1.3. Paying the $20 does nothing more than activate them and make them available.
[translation by crispin]