I saw Kenny Garrett here in Denver last week, and he walked on-stage with his sax on, carrying his case. He set the case down next to the piano and played. Later in the set they went off-stage for one of those pauses that encourage applause, and he kept his sax on and grabbed his case when he went off. He brought it back when he returned for the encore. As soon as the set was done, he put the sax in the case and walked out the front door of the club with it. His approach to security extends to the case as well as the sax!