Darn it, we upgraded our PSP to 3.51 and it turns out that "PSP-Vault.com":http://psp-vault.com says you can't go back now and run homebrew above this release without addition hardware. Amazingly there is a special "Pandora's Battery":http://www.psp-vault.com/Article1124.psp which unbricks and resets PSPs. You have to run a program on an already hacked PSP that converts a standard PSP into a jigkick battery.
# You run a program on a homebrew-enabled PSP that will convert a standard PSP battery into a jigkick battery. Note that you can't then use that battery normally - so you should use a spare one.
# You run a program to generate the unbricker memory stick image, built from the v1.5 update EBOOT (note that this, and the custom IPL, means the release is completely free of Sony copyright materials).
# You run some programs on a PC to install the image to your memory stick.
For us, we probably won't go to this trouble since the PSP is getting old now, but just be warned, before you update, read this and do the homebrew thing to preserve your options!