MADISON, Wis. -- I don’t know if Mayor Dave was at Wilco’s sold-out show at the Overture Center Saturday night, but it was a matter of concern for frontman Jeff Tweedy.

Eight songs into the band’s set, Tweedy pointed out that when Wilco played Duluth, Minn., the night before, their mayor was there and they even named Wilco an honorary Duluth band, although the band has “only played there like twice.”

“And how many times have we played Madison? Lots of times. And no key; no certificate. Nothing. Somebody’s really got to get on that,” Tweedy deadpanned. “We really like it here.”

Throughout its two and a half hour concert Saturday, Wilco played as if it was angling for a key to the city, and the band’s fondness for playing to a Madison audience was evident from the exuberance of the six musicians on stage.

Over its 15 years as band, the Chicago rock group has explored a varied range of sounds, from early alt-country tendencies to a sound influenced by classic rock, pop and folk. Ever restless, the band reinvented itself by pushing its music in a more experimental direction. And when it seemed Wilco had become a band preoccupied with turbulent sonic experiments, it switched gears again, putting out a melodic, folksy album followed by a fairly straightforward guitar rock album -- 2009’s “Wilco (The Album).”

Wilco established the tone for Saturday’s show early on, opening with the chugging rock of “Wilco (The Song).” Over the song’s playful rhythm, Tweedy sung, “Wilco will love you, baby,” and a sense of joyful openheartedness pervaded the mood of the evening.

Wilco then launched into another song off the new album, “Bull Black Nova,” a jarring, paranoid rocker with a clanging rhythm that recalls a phone being left off the hook. The claustrophobic “Bull Black Nova” was an abrupt transition from the lighthearted “Wilco (The Song),” but it signaled that the band was in the mood to rock out, and the set list for the rest of the night favored songs with driving guitars and opportunities for the band to unleash its unique wall of sound.

And that seemed just fine with the audience, who enthusiastically cheered the band on.

“You guys are rowdy,” Tweedy told the audience at one point, an observation that’s likely rarely made of audience members in the elegant Overture Hall.

“I Am Trying To Break Your Heart,” the opening track from the band’s breakthrough album, 2002’s “Yankee Hotel Foxtrot,” was an early high point in the set.

The band’s two multi-instrumentalists – Pat Sansone and Mikael Jorgensen – laid down waves of sound with buzzing, squeaking and humming electronics as drummer Glenn Kotche masterfully filled in the song’s spaces. It was easy to get caught up in the swirling acoustics as the incandescent candelabra-like lights that dotted the stage pulsed and glowed in the darkness.

But the exceptionally talented lead guitarist Nels Cline stole the show with a spectacular guitar solo during “Impossible Germany” that was so impressive that people jumped to their feet to whistle and applaud. Guitar solos can easily become indulgent, but I was impressed with the precision and grace of Cline’s playing, the way his playing served the song and how he was able to consistently wow the audience without going overboard by laying it on too much. Normally I get impatient for long guitar solos to end, but Cline is the rare exception when I would’ve been happy to hear more.

Wilco has undergone numerous lineup changes over the years – Tweedy and bassist John Stirratt are the only remaining from the original lineup. But the current six members have been playing together for several years now, and judging from Saturday’s show it’s evident they’ve melded into a remarkably tight musical unit. With the band’s stability, Tweedy seems to have become a looser performer. During “Hummingbird,” he freed himself from his guitar and sung with mic in hand, ending up jogging in place and twirling the mic by the chord.

Wilco kept the audience engaged throughout with older favorites like “A Shot In The Arm,” “Via Chicago,” “Heavy Metal Drummer,” “Kingpin” and “California Stars.” The band even reached all the way back to it’s 1995 album “A.M.” to play “Casino Queen.”

But those hoping to hear more from classic albums like “Being There” and “Summerteeth” were out of luck.

Instead, Wilco played most of its latest album. While newer songs like “One Wing” translated well live, I would’ve rather heard a number of other stronger songs in the place of “You Never Know” and “Sonny Feeling.”

There were some surprises in the set list. Wilco pulled out “When The Roses Bloom Again," which was recorded as a demo during Wilco and Billy Bragg’s “Mermaid Avenue" sessions but not released on those albums. Tweedy noted that it was the most requested song on the band’s Web site to play live.

Also, when the band returned for its encore, it launched into a strong cover of “Broken Arrow” by Buffalo Springfield.

The only big disappointment of the show was Tweedy’s decision to have the audience alone sing the majority of “Jesus, Etc.,” one of the best songs off “Yankee Hotel Foxtrot,” which is arguably the band’s best album.

The band played the song quietly so the tentative audience could group-sing the verses and chorus, and I kept waiting for Tweedy to step up to the mic and start singing to save the song … but it didn’t come until the very end, until it was too late to really salvage.

It’s not the audience’s fault – roughly 2,000 people gamely joined in. But the multitude of voices awkwardly resulted in a wan version of a powerful song. If anything, it affirmed the weight of Tweedy’s singular, raspy vocals, which fuel the song’s poignancy.

Although I wish the set list would’ve relied a bit less on the newer material to explore more of the band’s extensive catalogue, it’s hard to find much fault with a band that delivers 28 songs and leaves the audience wanting more.

In the end, it’s a testament to Wilco’s greatness that it can deliver a high-energy and riveting two and a half hour show and still not have time to squeeze in various other classics from its extensive catalogue. That’s not an issue many rock bands working today have.

Set List:

1. Wilco (The Song)
2. Bull Black Nova
3. You Are My Face
4. I Am Trying To Break Your Heart
5. One Wing
6. A Shot In The Arm
7. At Least That’s What You Said
8. Sonny Feeling
9. Nothing’severgonnastandinmyway (again)
10. Deeper Down
11. Impossible Germany
12. When The Roses Bloom Again
13. Country Disappeared
14. Handshake Drugs
15. You Never Know
16. Jesus, Etc.
17. Hate It Here
18. Theologians
19. I’m The Man Who Loves You
20. Hummingbird

Encore:

21. Broken Arrow (Buffalo Springfield)
22. Via Chicago
23. California Stars
24. Walken
25. Heavy Metal Drummer
26. Kingpin
27. Casino Queen
28. Hoodoo Voodoo