The easiest way to download your 2.71 firmware PSP would be to download the downgrader, plug your PSP into the computer using the USB cable, and run the executable you just downloaded. It will transfer all the proper files to your PSP in order to downgrade it to 1.50 firmware and also give audio commentary and some pictures of what to do while it is going through the whole process.
Why?
Why would you want to downgrade your PSP firmware you may ask? There are lots of reasons someone would want to upgrade their firmware. Homebrew software probably being the largest reason to upgrade. 1.5 firmware seems to be essential if you plan on doing development with the PSP, or running software developed and/or ported to the PSP platform.
Emulation is another reason. Sure alot of the stuff being emulated is technically illegal, there is legitimate uses for some of the emulators out there. Bochs for example runs linux, windows 95, and attempts to boot a couple of the bsds. Is there a use for this? absolutely not. Is it cool? Of course. Also, emulators play a large roll in development for other consoles. Most people cant afford the expensive development hardware that is needed to get their game on a console, so emulation is the best way of playing their work.
How?
Its easy really. Goto this url, and download the full version of the downgrader. I read you get the best results when you format your memory card pre-downgrade, and even better results when you use the default 32 meg card. So I did both and the downgrade started on the second attempt.
After you have your PSP setup, plug in the USB cable, and enable USB transfer in the Settings menu.
Go into my computer and find out which drive letter has been assigned to your PSP, then run the downgrader. Follow the onscreen directions. You will be asked which drive letter your PSP is, select the appropriate drive and continue on. All the files will be copied to your memory stick.
Once this is complete, goto the photo section and load up whats on the memory card. You will get 1 of 2 results, either a red screen which is good, or your PSP will lock up, which simply means you turn it off, and restart. Continue this process until you get the red screen. When you get the red screen let the PSP do its thing until it turns itself off.
Turn your PSP back on, you will be prompted with an error. Don’t worry about this error, just hit the circle button and continue on. You will have to reconfigure all of your settings, but once you are in, voila. 1.5 firmware.
Who?
Anyone running the 2.71 firmware can downlgrade their PSP, except for the people with version TA-082 PSPs. To check if you have one of these open up the UMD drive and look along the top, if you have a version TA-082 you will see writing along the top of the exposed motherboard. It may say ic10003. Do not attempt a downgrade if you have this version. All other versions will have no text and are good to downgrade.
Caution!
Proceed with caution. I may have succeeded with my downgrade, and so has many other people. However I am not responsible if you brick your PSP.