Along with fellow Houston musicians Joe Sample (piano), Wilton Felder (tenor saxophone) and Stix Hooper (drums), Henderson moved to Southern California and rebranded the group The Jazz Crusaders. Their sound owed much to hard bop, the dominant straight-ahead jazz style of the late '50s and early '60s, but the band didn't hide its time in Southern black churches, blues bands and R&B groups. That embrace of tuneful melodies and winning grooves, along with the unique tenor-sax/trombone frontline, made The Jazz Crusaders popular both in and out of the jazz community.
In 2004, Henderson told NPR's The Tavis Smiley Show about how he approached composition.
Actually, melody — see, I think first melody," Henderson said. And when you can hum it, then the next thing comes, obviously, the rhythm, man. See, once I get my melody, then I lay into my rhythm, and then fill all those beautiful harmonics and those inside harmonics it is. But I think melody — I've got to think that first."
As rock, soul and funk took hold — and along with them, jazz fusion — Henderson and the band adapted. The Jazz Crusaders became known for covers of The Beatles, Carole King and Sly and the Family Stone. The band dropped jazz" from its name, started working with vocalists (including Henderson himself), and embraced electric keyboard, guitar and bass. And, as The Crusaders evolved to more of a fusion style, crossover success took hold in the form of Billboard chart placings and slots opening for bands like The Rolling Stones.