Announcing the last scheduled number of his concert Saturday night, tenor saxophonist Joshua Redman informed the capacity crowd at Carnegie’s Zankel Hall that he had only that day noticed that he and the other two members of his trio, bassist Reuben R. Rogers and drummer Ali Jackson Jr., were all about the same size, had about the same coffee-colored skin tone (despite the leader’s name), and all with shiny, clean-shaven heads. “We look like an Afro version of [the mime ensemble] ‘Blue Man Group,’ so just for tonight I’m naming this ensemble ‘Brown Man Group.'”

I have heard Mr. Redman half a dozen times since his emergence 11 years ago at the age of 23; he was already a major talent, but until Saturday I was never able to get a bead on what he was doing. On one appearance he seemed like he was trying to out James Carter as a free jazz exhibitionist, at other times he sounded more like the Wayne Shorter of the 1960s.

Saturday night’s trio performance was, contrastingly, focused and succinct: Messrs. Redman, Rogers, and Jackson all knew where they were going and exactly how to get there. Mr. Redman is a commanding soloist, more than capable of holding the stage even in this most demanding of instrumental formats and in a concert setting where there’s no place to hide.

The first half consisted of four original compositions: “Twilight” (originally written as music for a performance piece by Anna Deveare Smith), “Hey Man,” “Two-Track Mind,” and a new, as yet untitled piece for soprano that suggested Scottish folk music. Mr. Redman’s current trio is essentially bebop, adapted into a personal language, and the sound of his tenor accompanied only by bass and drums is rooted in Sonny Rollins’s trio sessions of the late 1950s and John Coltrane in the same format on the 1957 “Lush Life” album.

Growing up, Mr. Redman never sounded like a prodigy going through his paces – he always seemed like a mature, complete musician. All of his pieces boast memorable heads and none rehash overly familiar chord patterns.

The second half of the concert was less serious than the first; for good fun. Mr. Redman evoked two great tenor-composer combinations: Coltrane playing Monk (“Trinkle, Tinkle”) and Stan Getz playing Antonio Jobim (“How Insensitive”). His own remaining originals were predominantly playful. “The One-Ness Of Two,” played on soprano, seemed suggested by Coltrane’s take on “The Inchworm,” and was primarily an inspired set of exchanges with Mr. Jackson’s drums. The final tune, which he was titling “BMG (Brown Man Group),” was an experiment: The piece changed time signatures every bar. He raced through 4/4, 3/4, 6/4, and other meters that suggested Dave Brubeck’s “Time Out” period – very entertaining.

Mr. Redman has a way of moving as he plays that resembles dancing, and suggests the he literally throws himself into the instrument. He is the horn, the horn is he.