Tether jailbreak iOS 6.1.3 to downgrade to 6.1.2?

I ended up getting a new phone, not by choice, I had an iPhone 3GS with an untethered jailbreak on iOS 6.1. But now that I'm stuck with this iPhone 4 on 6.1.3 the phone just feels useless and annoying. I was wondering if I could tether jailbreak my iOS 6.1.3 and then somehow use that to downgrade my iOS. Does anyone know if this is possible, and if so, how to do it? If not, is there another way I can downgrade? (I can't use SHSH blobs as when I got the phone it was on 6.1.3 therefore I have none saved.)

Get the iphone 5