The truism among big bands is that “the group that plays together, stays together.” Constant rehearsal and performance make a good band great, which is why some well-drilled student ensembles, like the Juilliard Jazz Orchestra (playing this week at Dizzy’s Club Coca-Cola) can sound better than all-star professional bands that get together for a one-shot gig.

Here in the jazz capitol of the world, some bands keep the past alive (such as Wynton Marsalis’s Lincoln Center Jazz Orchestra) and others look to the future (such as Butch Morris’s), while still others represent the vision of a single personality (Maria Schneider). But in terms of the here and now, the Vanguard Jazz Orchestra is it.

This week, the orchestra, which normally works Monday nights at the famous Seventh Avenue cellar, is playing for six whole nights – or what the band’s director and emcee, trombonist John Mosca, calls a “a week of Mondays.” This is a celebration of the 40th anniversary of the VJO, long known as the Thad Jones-Mel Lewis orchestra, which began rehearsals at the end of 1965 and opened at the Vanguard in February 1966.

On Wednesday, it opened the first set with a variation on “Sunny Side of the Street,” originally written for a rare French album with organist Rhoda Scott. The piece began with the rephrased melody on trumpets and counterpoint by the trombones. The saxophones (Dick Oatts, alto, Ralph Lalama, tenor) sat things out at the start but made up for lost time by taking most of the solos. The piece was very much in the Basie pocket; it even closed with a Count-ish three-note tag.

From then on, the emphasis was on Bob Brookmeyer’s music and on returning soloist Tom Harrell, star trumpeter and Vanguard veteran. The group launched into “American Express,” written for the band’s 20th anniversary in 1985. It later played “ABC Blues,” from the band’s first session. Both are Brookmeyer masterworks that change tempos and moods several times and spotlight soloists and ensemble playing. Some passages are deep in the Mississippi Delta; others seem to have been concocted by musical mad scientists in the Bauhaus.

Mr. Brookmeyer’s arrangement of “Willow Weep for Me,” from the premier album, is a similar advertisement for the inherent possibilities of jazz-pop standards. From its famous whole-tone introduction (with bass commenting on horns) through its melody (played Mr. Harrell on flugelhorn, taking over from the Jones, who did so on cornet), Mr. Brookmeyer put as much of his soul into this recasting as he did into any of his own original works.

It was time for a break from the Brookmeyer pieces, heavy (but still swinging) as they were. Mr. Mosca called for “Sao Paolo,” an original Mr. Harrell wrote 20 years ago during his own tenure in the Mel Lewis Orchestra. It was a light, airy bossa nova, with the melody stated on flute and muted brass. Mr. Harrell took the main solo on open-bell trumpet.

Then there was just time left for a short zinger, one of Jones’s most to-the-point pieces – “Once Around,” also from the first album. The VJO’s reading was even faster than the original, and Gary Smulyan’s baritone saxophone solo was more exciting than that of Pepper Adams – it’s hard to imagine how he can make such a big horn move so fast.

The Vanguard Orchestra plays through Sunday this week, but happily, they will be ensconced one flight down for all foreseeable Mondays to come.

Until May 15 (178 Seventh Avenue South, at West 11th Street, 212-255-4037).