Long-time member Coleman Hawkins is said to have perfected the tenor saxophone. When he traveled, local saxophonists flocked to the bars he played in order to challenge him. He out-performed everyone. Unfortunately, his characteristic rich tone suits itself to the long notes of smooth jazz, and smooth jazz rarely swings. The "Esquire Bounce" is the only swinging song of his that I could find.
Hawkins quit Fletcher's band in 1935 to go to London. Rumor is he grew tired of the constant battle to be the best in the States. One of his challengers, Lestor Young, briefly replaced him. The Kansas boy's lighter style upset the rest of the band, though, so he left just two months after joining. Their loss. That light touch suits itself to dancing, as in "I've Got Rhythm" with Count Basie.
From left to right in the picture are an alto, soprano, and tenor.