In 1963, DownBeat magazine began using the phrase “Talent Deserving Wider Recognition” in its annual jazz poll. It was a useful idea, if a bit relative. Are there any important living jazz (or even classical) musicians who don’t deserve wider recognition? In contemporary American culture, it seems the only way an artist can truly become “widely recognized” is to appear on a reality television show, be chewed out by Simon Cowell, or arrange to be adopted by Madonna.

In jazz, as in classical music, there are at least two different kinds of recognition, which we might call internal and external. The excellent trumpeter Terell Stafford, who is appearing this week at the Village Vanguard, is a good example of a player who has achieved lots of the former but is overdue for more of the latter. He is generally the first trumpeter whom bandleaders call when they want someone dependable and flexible, who can play virtually everything, and is always inspired in the process. (This summer alone, I’ve seen Mr. Stafford with two different bands led by Frank Wess in two separate clubs.) On top of that, he runs the jazz program at Temple University. Sounds like widespread recognition, right?

Well, Mr. Stafford almost never appears as the leader of his own band in a major New York club, and has only made a handful of albums under his own name, as opposed to the 50 or so on which he has played as a sideman.

Yet Mr. Stafford’s quintet is a real working band with its own repertoire and personnel — not just a bunch of guys he calls at the last minute when a gig pops up. The quintet’s most recent recording is a club show from Minnesota in 2005, released last year and called “Taking Chances: Live at the Dakota” (MaxJazz). This week at the Vanguard, Mr. Stafford is featuring his regular band, with Tim Warfield on tenor saxophone, Peter Washington on bass, and Dana Hall on drums. On opening night, Tuesday, his regular pianist, Bruce Barth, was delayed (curse you, American Airlines!) returning from a gig in Europe and was replaced by the young Gerald Clayton, who works with Mr. Stafford extensively in the Clayton Brothers band. Nevertheless, the band was so tight that nearly every tune was something special.

The opener, Mr. Stafford’s “Berda’s Bounce” (from his 2003 release “New Beginnings”) was a basic, fast hard-bopper in the Jazz Messengers mold, and a particularly catchy one. Like much of the quintet’s repertoire, it’s dependent on a powerful frontline of trumpet and tenor. Mr. Stafford announced that he prefers leading a band in which everybody writes, because “it takes some of the burden off the leader.” One example was an intricately rhythmic composition by Mr. Hall, “Paper Trail,” in which the drummer-composer’s own solo was carefully woven into the fabric of the tune.

But the outstanding original, both at the Vanguard and on the live album, is Mr. Barth’s “Pegasus,” which features classical allusions in both form and title. Mr. Barth, who spent most of 2007 on the road with Tony Bennett, cast it in a very subtle 3/4; one wouldn’t notice the waltz time signature without a concerted effort. Mr. Warfield soloed on soprano saxophone in this piece, his style more withdrawn, in the manner of more recent Wayne Shorter music. “Pegasus” constantly moves from inner to outer, introverted to extroverted, and every solo, including those by Mr. Stafford and Mr. Clayton, followed this trajectory.

While the originals, especially the 3/4 waltz, were outstanding, the songs that really galvanized the audience were two unusually thoughtful treatments of standards, “Taking a Chance on Love” and “Blame It on My Youth,” the first for its complexity, the second for its simplicity.

Nearly every trumpeter working today owes a debt to Miles Davis, something Mr. Stafford acknowledged by including “I Don’t Want To Be Kissed” on his previous album. But he goes a step further back by paying homage to one of Davis’s own inspirations, the pianist Ahmad Jamal. On “Taking a Chance on Love,” the rhythm section starts with a paraphrase of the vamp to Mr. Jamal’s signature, “Poinciana,” before the horns enter, alternating between Mr. Warfield’s soprano and Mr. Stafford’s flugelhorn. But instead of delineating that Brazilian melody, they lay out Vernon Duke’s original “Taking a Chance on Love.” On the album, it seemed merely clever, but in person, it was inspired.

At 41, Mr. Stafford is steadily maturing into an exceptional balladeer: When he played the Vanguard with Mr. Wess in May, his solo was Willard Robison’s “Old Folks,” and on Tuesday he topped himself with another classic song, “Blame It on My Youth,” by one of the more extreme characters of American music, Oscar Levant. His approach to the melody, played on flugelhorn, was very vocal, reflecting not just mentors such as Miles Davis and Lee Morgan, but Ruby Braff, Warren Vache, and other vocalists of the horn.

After singing the tune, he improvised with a wide range of effects, gradually picking up the speed and intensity, trying to push the tempo as far as he could without dropping the other shoe and abandoning the ballad ideal. Mr. Stafford kept driving right up to the edge of the cliff, but he unfailingly showed the restraint to pull back just before reaching the edge. And he didn’t just do it once, but again and again, until the audience went wild with suspense.

All the while, Mr. Clayton fed Mr. Stafford with just the right chords and tempos. In his own solo, he went for the same effect, striving for that dramatic tension between slow and fast, intimacy and transgression. If, at 24, Mr. Clayton hasn’t yet achieved quite as perfect a balance between the two as Mr. Stafford has, it’s certain that he will soon. In the meantime, we can blame it on his youth.

wfriedwald@nysun.com