Okay. After some serious digging on YouTube, following a hunch that Chet Atkins may have had a version of it, I did manage to locate Chet Atkins “Armens Theme” which doesn’t quite have that “Middle Eastern flavor” I remembered, but that is the tune that I always tend to confuse with the Third Man Theme.
Now I can rest! Don’t you just hate it when there’s something like this hanging over you? 
yes … a year or so ago I went nuts over misirlou!
Are you thinking of the Dick Dale Pulp Fiction version? That one stomps!
I believe there’s something about music from the Mediterranean and Near Eastern countries that has a “grabbing power” unlike other music. Take Brubeck’s Blue Rondo A La Turk as an example. He has another one called Nomad that is similarly fascinating. I haven’t been able to locate a version of it at YouTube.
Anyway, your thread has been great fun and maybe some other tunes on the edges of our consciousness will spring forth as a result.
True, although Welles did create the “Swiss Cuckoo Clock” line, perhaps the most famous part of the movie, even though it is factually wrong on several points: The Swiss did not make cuckoo clocks and they were a strong and feared military force at the time of the Borgias.
I love how music can modify mental state, and I do agree that there is something compelling in middle eastern music, especially drumming.
I actually have a list on my ipod of music that will relax me no matter what - and it is a blend of everything except rap, country and bubblegum pop.
I have another fun piece that is one of my favorites - Chira Xur you can just hear the horse =) The same guy has a cd out of his group covering modern rock music on mongolian instruments. He has a killer version of When the Levy Breaks =)
Surely you’re familiar with Paul Pena and his Genghis Blues documentary. You might find Amazing Grace using throat singing overtones and 5 Year Old Boy Throat-Singing worth a listen.
If you like that zither music, check out Bryan Bowers playing the autoharp.
The autoharp is a chorded zither, and he’s been the best in the world for decades.
His harps are modified for certain keys, and he uses fingerpicks, for both digging in and picking the strings, and slapping at the strings.
Been listening to him since the early '70’s.
David