Tommy1994! has posted about a 3.71M33 to 1.50 downgrade procedure on the QJ.NET PSP Development Forums. The special thing about this downgrade procedure is that it works even without using the Pandora battery.

This downgrade procedure by Samhain reportedly works for PlayStation Portable units that have TA-079 and TA-082 motherboards. You'll need an original firmware 1.50 file to make it run. This particular file isn't included in the download below so you'll have to go find one for yourself.

Please keep in mind that this has only been tested on TA-079 and TA-082 PSPs so far. Check out http://forums.qj.net/f-psp-development-forum-11/t-releasedowngrade-371m33-to-150-without-pandora-122444.html for instructions.