I just got a new Epi LP standard and am adjusting the action as it was rattling when I got it. After adjusting it, I sometimes get a rattling noise on every string. It isn't fret buzz and sounds like its coming from the bridge end. What is this?

EDIT: The title should not have 'Fret' in it
Epiphone Les Paul Standard
Fender MIM Standard Strat
Fender Deluxe Reverb
Digitech Bad Monkey
Electro Harmonix Big Muff
Ernie Ball VP Junior 250k
Dunlop Cry Baby Wah
Probably just a loose part. I had this problem with a loose washer in the headstock. Just try finding a string that makes it buzz and use that to try and find out where it is coming from