Wow - sorry for the grave digging here but there are a few great Q spots in Tucson.
My #1 favorite is Mr. K's on South Park and then the place that used to be called Tom's BBQ at Craycroft and 22nd.
Mr. K's is awesome food - slow smoked over mesquite right in their yard with several barrel smokers. No screwing around at either place with broiling/boiling/backing and then drenching in sauce. The pulled pork at the new place is phenomenal but Mr. K's > * for brisket, chicken, sausage, etc.
Mr. K's also has some delicious cobbler and their collard greens are the best I've tasted.