Upgrade from 4.1 to 4.3.3
The prior reply is UNTRUE, you can upgrade and downgrade as you see fit, signed or not, there are a few tricks to get it done. If you have the latest version of redsn0w, you can create a version without a baseband, complete a restore of 4.3.3, then do a tethered boot, it will get you into the os, then you add wireless, go to jailbreakme.com, run the jailbreak, restart the phone with iFaith, and run the shsh blob dump, and then build a signed ipsw file, then you can restore whenever you feel like it.
I do this for our customers all the time, and we do not have any problems. I just did another about 5 minutes ago.
Sometimes you need to do a little more research and testing and fussing around to get it to work, you cannot always believe these people on here, a lot of the time these people know what they are talking about, and LOTS of times they DON'T!!!!!
I usually don't say anything, I just let others do and say. But sometimes I feel that I need to chime in and correct a BIG mistaken statement.