If other doublers are like me, they have certain exercises they do on certain instruments. But they don't try those exercises on their other instruments, even if it would be an easy switch.
Last night at the Deer Head Inn, Lew Tabackin was playing his ass off with his "International Trio" of Boris Kozlov (who used to play in my band Terra Mars) on bass, and Mark Taylor on drums. During the break Lew sat down at our table to continue a conversation he and I were having earlier.
Since we were a table of sax players (with my husband Gil, and even my brother Brian, who was visiting, used to play bari in high school) we were talking shop, and Lew mentioned that he does the Marcel Moyse flute exercise (longtones descending in half steps, 2 at a time repeated) on saxophone starting on the lower G and going down to Bb, with the loosest embouchure possible.
I thought that was a great idea and I plan to implement it immediately.
BTW if you are not hip to the astounding tenor and flute mastery of Lew Tabackin, I suggest you immediately check him out. He is a true Artist.