It seems like all the major carriers cooperate to some degree. This is an interesting article from back in 2012, with many good quotes from UPS/DHL/FedEx: http://www.talkleft.com/story/2012/11/16/183045/99/crimenews...

The parts about opening up direct database access to law enforcement was disappointing but not surprising.

USPS in theory actually provides better protection because US mail has stronger legal protections than handing your package off to a private entity.