I think you may be thinking more along the lines of a "donner kebab"?
Adana kebabs are seldom greasy at all. Lean-ish minced lamb or beef cooked on a stick over hot coals, served on/in oven baked turkish bread with lots of fresh salads:
http://www.julietmae.com/product_ima...bab%20urfa.JPG that kinda thing.
Yeah "kebabs" though...are pretty hit and miss, and more miss than hit...cheap quality products, poor instore hygeine, processed meats...yech. If you get a good quality one they can be great, but there's so many shitty stores selling them.