"Whoopin' Blues" (PDF) from the Leroy Jones album, New Orleans Brass Band Music: Memories of The Fairview & Hurricane Band, and compilation, Putumayo Presents New Orleans Brass.
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Until somebody can confirm the trombonist for me, without a physical copy of this album I have to assume that this solo is played by Craig Klein, who has gone on to play with Bonerama. Klein is credited as a band member in this album review, however it also suggests without specification that trombonist Katja Toivola, the wife of trumpeter Leroy Jones, makes a guest appearance on one tune. So it could be her playing this solo. I do not know.
UPDATE: Special thanks to Anja Toivola for clarifying that Katja Toivola is featured on "Just A Little While To Stay Here."
"Whoopin' Blues" was written by clarinetist John Casimir of the Young Tuxedo Brass Band, and the second half of the melody features the signature John Avery call and response line. And while the trombone solo predominantly uses the Eb blues scale, the phrases stay very linear, much like the original melody. The second half of the trombone solo features growls, triple tonguing, and peak high notes, especially in a bar 17 as it leaps even higher to one-up the previous phrase, techniques that are sure to light up a blues solo.
Here is a YouTube video of Leroy Jones leading the Hurricane Brass Band through a performance of this tune.
Recommended Reading: Roll With It: Brass Bands in the Streets of New Orleans by Matt Sakakeeny. Published by Duke University Press.