This pipe turned up on a recent eBay auction, and although I was not inclined to bid on it, I did grab the photo for curiosity's sake. Not really a good photo, but still.
The Kaywoodie company was very good at coming up with any excuse they needed never to waste a piece of briar. You got a leftover piece that might make a pipe except it's too narrow? Don't throw it away! Let's make a pipe anyway and come up with a good reason for it later.
This is the EZ Set Vest Pocket pipe in shape #66. It looks sort of flattened because it was, so it would fit in your pocket more comfortably (yes! really! we meant to do that!).
I find a study of Kaywoodie pipes fascinating partly because of all the reasons they came up with never to waste a piece of briar.
Oh, by the way, this is the white briar finish, "the feel of briar with the look of meerschaum," ostensibly for those who wanted the classic look of meerschaum but the smoking qualities of briar, as if something was wrong with the smoking qualities of meer. I think the real reason is that they had some wood that was going to look horrendous without a think coat of paint, and this was the best they could come up with.
You might think from this post that I have some sort of grudge against Kaywoodie, but that is not the case at all. I have several Kaywoodie pipes and smoke them often. I just don't have any reason not to call 'em like I see 'em.