Three guys walk into Birdland — stop me if you’ve heard this one. The first guy is a jazz fan and wants to hear a terrific instrumental soloist; the second guy loves the Great American Songbook and would love to hear an outstanding singer; the third guy, frankly, could use a few laughs and would rather be going to a comedy club. The punch line is that they’re all in luck because John Pizzarelli is playing tonight.

Mr. Pizzarelli is indeed all these things — guitarist, vocalist, and tummeler (as his fellow Italians say) — not to mention, in other guises, songwriter and radio host. Lately he’s also become something of a one-man media blitz: This week he headlines at Birdland with a full orchestral contingent, the New York All-Star Big Band, and then, with barely a Monday night off, he begins a monthlong run at Café Carlyle. He’s also just released two albums, “Dear Mr. Sinatra” (Telarc), in which he sings with the Clayton-Hamilton Big Band, and “Generations” (Arbors Jazz), which finds him playing with his father, the legendary guitarist Bucky Pizzarelli. (The younger Pizzarelli may be the jazz world’s most famous family man: In addition to recording regularly with his father, his May stint at the Carlyle will co-star his wife, the fine singeractress Jessica Molaskey. His brother, the bassist Martin Pizzarelli, is a permanent presence in his rhythm section.)

The Birdland show is listed on the club schedule as spinning off Mr. Pizzarelli’s Sinatra tribute album, but he does only three tunes from it. Ironically, this is one of the few times I’ve seen Mr. Pizzarelli not tell his famous anecdote about the time he opened for Sinatra and got to meet the Chairman in a choice encounter that was considerably shorter than the time it took you to read this. (My one meeting with Mr. S. was even more succinct, by the way.)

The art of covering Sinatra is a fine one. Whereas Tony Bennett, on 1992’s “Perfectly Frank,” concentrated on the great standards found in Sinatra’s groundbreaking concept albums, Mr. Pizzarelli attempts the riskier task of going straight for Sinatra’s signatures and the songs specifically written for him (though thankfully, he, like Mr. Bennett, had the good sense to avoid “Strangers in the Night” and “My Way”).

Tuesday at Birdland, Mr. Pizzarelli opened with three Sinatra staples, leading off with Lew Spence’s “Nice ‘n’ Easy,” which, like most of the arrangements (by bassist and conductor Jeff Hamilton), are equally inspired by Count Basie and Nelson Riddle. The one that’s most radically re-thought is “I’ve Got You Under My Skin,” which Sinatra transformed from a torch song into a swinger and which John Clayton and Mr. Pizzarelli have reworked into a tranquil, medium-tempo tone poem for jazz orchestra. All it needs is tuba and French horns to make it sound like Claude Thornhill or Miles Davis’s Birth of the Cool band.

The rest of the show is drawn from Mr. Pizzarelli’s other bigband albums on Telarc, such as “The More I See You,” which he introduces as “My mother’s favorite song,” fighting back mocktears. The arrangement (by Dick Lieb) is anything but sentimental, percolating slowly to a dynamic finish. There’s also an ingenious medley of two “Baby” songs from the Nat King Cole songbook — “Baby All the Time” and “Gee, Baby, Ain’t I Good to You” — that suggest what might have happened had Cole and Basie ever officially collaborated.

Mr. Pizzarelli culminated the opening set with his epic tour de farce, “I Like Jersey Best,” a deliberately innocuous jingle that has been inflated through the decades to include a series of imitations of pop icons and now, to big-band proportions as well. The latest bits include a juxtaposition of Mr. Pizzarelli’s impressions of Billie Holiday and Madeleine Peyroux (they sound mysteriously similar) and Johnny Cash, in which he mimicked the man in black’s facial expressions and powerful gait. As with most of Mr. Pizzarelli’s comedy, trying to capture it in print only does it a disservice; there were a lot of “American Idol” gags, including one in which he asked the crowd to vote for its favorite member of the saxophone section: “and there’ll be only one left by Saturday night.”

You might think Mr. Pizzarelli would reserve his brassy, extroverted side for his nightclub performances and save his intimate and romantic side for instrumental projects like the duets with his father. This is not always so: A highlight of the Birdland show arrived when Mr. P briefly quieted the party atmosphere and noisy, Jersey-loving crowd long enough to do a warm and personal “I Thought About You,” with just voice and guitar.

The guitar duos with Bucky Pizzarelli also kick plenty of tuchus: The Benny Goodman favorite “Avalon” (which also appears on “Generations”) was a showcase for guitar, in which he displayed more instrumental chops than all of the 16 other guys on the stand put together, dashing out octaves on top of octaves and quoting Goodman’s shout chorus. The two-guitar version is possibly even more exciting; by the climax, the two Pizzarellis’ seven-string instruments were as hot to the touch as Paris Hilton’s credit card.

Although he has sung a few love songs very movingly, Mr. Pizzarelli is still a better balladeer as an instrumentalist than as a vocalist. “Generations” reaches its ballad peak with the second track, “Polka Dots and Moonbeams.” Senior starts the melody on the lower strings, then goes up an octave at the bridge. After the melody, Junior jumps in with a dazzling double-time chorus, playing the harmonics by tapping out the notes, assimilating ideas from Tal Farlow and Stanley Jordan. Like much of the collective musical legacy of the Pizzarellis, it’s both technically astonishing and emotionally moving.

John Pizzarelli wound up the opening show with a hard-blowing “Route 66,” in which much of the band got to solo, including the tenor saxophonist, Gary Keller, and the trumpeter, Jim O’Connor. It was a rousing finale, and I know at least three guys who were very sorry to see it end.

Mr. Pizzarelli begins his monthlong engagement at Café Carlyle, in tandem with the vocalist Jessica Molaskey, on May 1 (35 E. 76th St., between Madison and Park avenues, 212-744-1600).