His association with David Letterman, which spanned 35 years, began in 1980 as a stage manager on "The David Letterman Show" (NBC). He rejoined Letterman with the launch of "Late Night with David Letterman (NBC)" in 1982, remaining with it and "Late Show with David Letterman" (CBS) for their entire runs. Henderson frequently participated in the on-screen antics and sometimes was the star of short segments recounting his humorous adventures in New York. Henderson's "theme" music on the show was "Milestones" by Miles Davis.