Italian parcel post

[Butterfly]

I have been sorting "on piece" kiloware and ran across some Italian parcel post stamps attached to portions of waybills. 
The stamps have left and right halves, with perforations dividing them.  I only have the left halves. They are the ones kept as a receipt by the person sending the parcel. (or so I read somewhere on the internet)  When sending a parcel one apparently fills out a document called a waybill which has the addresses involved, etc. and onto which these parcel post stamps are affixed.  Then the postal clerk splits the pre-perforated document so that the stamps on the left can be given to the sender and those on the right attached (somehow?) to the parcel. 
Here are the front and back sides of some that I have.


Note that different waybill types are present.  They all appear to be dated 1967 or later.
I checked on ebay for waybills, but couldn't find an example. They have all been cut and/or torn into strips so that the parts of the waybills to the left and right of the stamps aren't seen.

Note also that normal practice seemed to be to use scissors for separating rather than relying on the stamp and waybill perforations lining up perfectly. 
Surprisingly, Scott says that the right half stamps are more common.  Before today I have mostly seen the left half ones.
They also all postdate the last date mentioned by Scott (1966) for these stamps.
 
Lots of questions here and not many answers. Sorry about that folks.
Hoping to learn more with time. 

[Butterfly]

After some sleuthing on ebay I found this example, which goes by the name of "Italian parcel post card".
It went to Israel, so the left side cards must be sent to the destination.

[mourningdoves]

Informally, I'd say that I have more of the "halves" that appear on these waybills than I do of the other halves: maybe in a 3-to-2 proportion. Also judging from my accumulation of Italian parcel post stamps (which are patiently waiting for me to make album pages worthy of them), most of the ones I have from before the mid-1950s were torn at the perforations like they were meant to be, not cut with scissors; maybe cutting them was a later innovation.

I have a couple of parcel post halves on waybill fragments, but nothing anywhere as complete or informative as the one in your second illustration.

The singer for an exceptionally trashy hard-rock band called the Tubes (perhaps best-known for their 1977 opus "White Punks on Dope") was one John Waldo Waybill, whose stage name was Fee Waybill. Turn that pseudonym around and you've got a fine capsule description of these stamps' purpose.