Letterman has been doing this particular shtick of late, probably in imitation of some of the old time comics. It consists of following the punch line with placement of the palm, fingers together and pointed downward, against one’s side above the waistline accompanied by a very slight raising of the shoulder on the same side.
Does anyone know who originated this move and what it was supposed to mean?
Isn’t that a play on Ed Sullivan?
Dunno about Ed Sullivan, but it conjures an image of the Church Lady for me.
It doesn’t mean anything. That’s the beauty of it! 
Isn’t it him saying “it’s so funny, his sides will split”? I kind of thought it was that, though now I think about it, I’m probably way off.
Jack Benny?
Is he about to break into a verse of “I’m a Little Teapot”?
I have a mental image of Henny Youngman or Jackie Mason doing this, but I’m not sure. That’s why I posted this question.
As I recall, Letterman’s been doing some sort of post punchline-rimshot accent move for years, it just varies as to the actual action. Years ago it was a sort of horizontal air punch toward Paul & the band. I don’t know if his current move means anything, other than being a silly move just for the sake of it.
Now that you mention it, that arms akimbo stance brings back memories of Sullivan. Because he broadcasts from the Ed Sullivan theater?
Giloooooly.
He’s imitating Jeff Giloooooly? Wouldn’t that involve whacking somebody across the knees?
No, I was referring to the way he used to insert “Gilooly” or “Buttafuoco” into his monologues for a cheap laugh. Not the same thing, I guess.
Ed Sullivan kinda seems right.
Ed Sullivan looked like he had his shoulders hunched up toward his ears and his arms held close to his sides. I don’t ever recall seeing him do this move.
It’s a comic’s move; Sullivan was not a comic.
I nominate this as understatement of the week.
My take on it is just that it’s another of Letterman’s efforts to create something out of whole cloth. His attempts at catchphrases, like “in my pants” for example, are mostly for the silliness and can’t really be analyzed beyond the absurdity involved.
If there’s a deeper meaning or some arcane reference to some old schtick, I would be surprised. I see it as gimmick du jour pretty much the way that the gal bringing him food while he’s doing the intro to the show is a gimmick that he’ll try to run into the ground.
I, for one, have quit laughing at “Great Moments in Presidential Speeches” except for whatever they’ve done to the JFK footage. I realized long ago that GWB is no orator.