PSP firmware update 3.95 update includes the following:
While playing PSone games on your PSP, you can now customize how the buttons are assigned by going to [Controller Settings] > [Assign Buttons] and select [Custom].
You can now quit Remote Play and choose to turn off your PS3 or leave it on after quitting. This is useful if you are performing a download and want to quit Remote Play, but still want your download to continue on the PS3. Select [Quit and Turn Off the PS3 System] or [Quit Without Turning Off the PS3 System] from [Quit Remote Play] when you press the HOME button on the PSP system.