neur0n has released updates for both of his custom firmwares! Both 6.37 ME v7 and 6.35 Beta v18!
Like the others in the past, 6.35 is for PSP 2000 models only, but its update brings some cool improvements:
• Adding PluginManager to the VshMenu
• Removal of “Execute BOOT.BIN” option from RecoveryMenu
• Update of the NidResolver
• And supports custom PS1 DOCUMENT.DAT files
Of course, v7 of 6.37 ME has the same updates of:
• Adding PluginManager to the VshMenu
• Removal of “Execute BOOT.BIN” option from RecoveryMenu
• Update of the NidResolver
• And supports custom PS1 DOCUMENT.DAT files

To install the 6.37 ME v7 custom firmware, first, you need to install CFW or HEN like 5.00M33 or 6.35PRO onto your PSP, and then:

• Copy UPDATE folder at ms0:/PSP/GAME/.
• Put 6.37 official update at ms0:/PSP/GAME/UPDATE/637.PBP .
• Run installer from xmb.

What is probably the best feature on this is that if you hold the Right trigger whenever you turn your PSP on, it turns it to the recovery menu like most custom firmwares. But when you hold the Home button, you can boot official firmware!

Discussion: Here
Source 1: Here
Source 2: Here
Download 1: Here
Download 2: Here

Just yesterday, RoxFox64 met up with Hellcat and Davee who were in the final stages of making their new, signed downgrader. As it turned out, he had upgraded to 6.35 from 6.20 recently and needed to use it, imagine that coincidence! After waiting for Davee to give him the compiled version to test, he was more than happy to see that it had worked 100%!
With this downgrader, it will be very simple, and very safe, to downgrade from 6.35 to the 6.20 firmware!

From the ReadMe:

[What does it technically do?]
It uses the utility/power exploit to gain kernel access and reboots into the updater with a special PRX running. This PRX uses the pspdecrypt functionality to decrypt the updater PRX when needed. This allows the updater to boot in the newer firmwares.
So, in order to use this you need the official update for OFW 6.20 (SPECIFIC TO YOUR MODEL)
Installation is very simple:
Place the 6.20 update in X:/PSP/GAME/UPDATE/
and extract the downgrader’s folder into X:/PSP/GAME/

Why OFW 6.20?
Currently, 6.20 is the latest firmware we have full Kernel access on. This is the firmware you’ll find the absolute most functionality on along with HEN TN-C.

Discussion: Here

Downgrader Download: Here
6.20 Official Firmware (1000, 2000, 3000): Here
6.20 Official Firmware (Go!): Here

Well, it turns out that Sony has an update to add to the overall system stability and help out with preventing piracy that can be enabled with the latest pseudo-signing tricks that the PSP hacking community (most notably Mathieulh) has sent out. It’s said that our signed homebrew will work on all of Sony’s official firmwares, though, right? Well, does it work?
The answer is yes, our homebrew does work! This is great news! But, what does this new firmware add? Well, it adds preventative measures to using an HEN to enable homebrew launching from the XMB and a few other naughty PSP homebrew. So, should you update to it? For the first time ever, I think we can safely say that if you want to, go ahead. There’s plenty of homebrew that works and it will take very little time for a new release of the HEN to work on these official firmwares. Sorry Sony, but you cannot stop what has started…

Source: Wololo & Sony

Discussion: In the forum