Downgrade 3G 3.1.2

[ii Technicolor]

So I tried to jailbreak my 3g 3.1.2 iPod touch and blackra1n was unsuccessful. I am wanting to downgrade my firmware to 2.2.1 so the jailbreak will work however the only version of 2.2.1 that I can find is for the 2g. Will it work
anyway?