Background, was running my Iphone 4 with 4.2.1 and tethered jailbreak using redsn0w 0.9.6.4b. I wanted to update it to 4.3.3 to both get rid of the tethered boot (ie, to boot up the phone, it must be connected to my Macbook and I must go through a keypress kombo (not the Konami-code ;) ) and to get the convenience of Wifi-hotspots.
Itunes didn't like me though so it kept saying "this device is not eligible for the requested build" when it came to the 'verifiying with Apple' stage. Tried lots of things, and I had the latest Itunes etc. This accumulation of tricks I found on various sites is what finally helped:
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sync and backup the phone first! (sync, then rightclick and choose 'backup', maybe not necessary with both?)
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Downloaded the 4.3.3 restore IPSW (google for it)
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Removed the gs.apple.com entry in hosts-file (entry added automatically when jailbreaking, if Itunes finds it, it will stop with error 1013); enter the following and then quit and save by ctrl+X, then Y, then enter
sudo nano /etc/hosts. -
switched off the phone
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plugged it in with USB
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entered DFU mode (same as when you jailbreak: power 5 sec, power+home 10 sec, home 5 sec, don't let go of buttons between). Now the phone will show up in Itunes
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hold alt/option + command buttons when pressing the 'restore'-button in Itunes; this will let you choose what firmware to restore from
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point to the 4.3.3 firmware you downloaded
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then Itunes will process and work and finally the phone will boot, completely empty w firmware 4.3.3
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In the dialog 'Set up your iphone' you can choose to restore it (poor choice of words) from the backup that you took right before this procedure
After all this, I jailbroke it with the 4.3.3 untethered, reinstalled Pkgbackup and let it restore the jailbreak-apps and settings I had.