iFaith has a protection that you don't use it on the wrong firmware to protect you. Bluefreeze, a tool written by a group called The Private Dev Team, modifies the firmware version (and firmware checksum) in the iFaith certificate file, so that this check gets disabled. By doing so, you can install any firmware version on your device, even without having saved the SHSH files. The problem by doing so is that you actually install a firmware without signatures, with all consequences. This is what is known as a Tethered Downgrade.
Bluefreeze asks you to build and browse to two ipsw's one signed properly and one not signed. Then Bluefreeze swaps the properly signed img3 files in the properly signed firmware file with the incorrectly signed img3 files in the unsigned ipsw thus resulting in an ipsw file with properly signed img3 files. This firmware file is used for the downgrade.
Having an incorrectly signed firmware installed won't let you boot of course. But because the limera1n exploit ignores incorrect signatures we can use the limera1n exploit (DFU mode, then using redsn0w) to boot up your device. The problem is only that you have to repeat this every time (similar to a tethered jailbreak), so it's not a downgrade you would want. This should be your last resort, and only if you absolutely need a downgrade.
This way a downgrade to iOS 4.3, 4.3.5, or 5.0 from 5.0.1 is possible. Supported devices are iPhone 3GS, iPod touch (3rd generation), and all A4 devices.
Installing a firmware version using this method (without valid SHSH blobs) is incompatible with an untethered jailbreak. Each time the device boots, the bootrom validates the SHSH blobs for LLB, LLB for iBoot, and so on. Therefore, the image validation function must be patched or bypassed with an appropriate bootrom exploit payload on every boot or the device will be forced into DFU mode.
With this method you can install a firmware for which you don't have SHSH saved for some tests, for example if you're a software developer and need to do some tests on a specific version.