Jimmy Eat World. (Courtesy of the 9:30 Club/Courtesy of the 9:30 Club)

It’s made nine albums during its 22-year recording career, but Jimmy Eat World is still defined by its 2001 breakthrough, “Bleed American.” Wednesday at a sold-out 9:30 Club, the Arizona pop-punk quartet dealt capably with that album’s preeminence. It helped that the group’s new “Integrity Blues” is its best effort since that 15-year-old benchmark. While the recent material provided a contrast to the older stuff, it wasn’t a jarring one.

Jimmy Eat World doesn’t digress, improvise or otherwise fool around; it played 24 songs in 95 minutes. The set was structured around the four best-loved songs from its best-known album: “Bleed American” came second, after “Get Right,” an “Integrity Blues” highlight. “A Praise Chorus” arrived about an hour later. Then “The Middle” and “Sweetness” began and ended the three-song encore set, flanking “Sure and Certain,” another winner from the new album.

That might sound calculating, but singer-guitarist Jim Adkins and his cohorts made it feel natural. The band’s style barely distinguishes it from the many other 1990s-spawned combos sometimes termed “emo” (a generally reviled term). But the group’s punchy tunes, yearning lyrics and singalong choruses never seem contrived. Its essential unity was demonstrated by those occasional passages when guitarist-singer Tom Linton took the lead vocal. The switch was barely noticeable, aurally or conceptually.

Far more intricately produced than its predecessors, “Integrity Blues” features strings, keyboards, vocal chorales and cascades of strummed acoustic guitar. The band didn’t attempt to reproduce all this onstage, although Adkins did unplug for a few songs. Most of the embroidery was designated to touring member Robin Vining, who played primarily keyboards but also guitar (and left the stage during the simplest older tunes). His most crucial contributions were the high harmonies that buoyed such new tunes as “You With Me.” These didn’t exactly turn Jimmy Eat World into the Beach Boys, but proved the band can handle more than unison singing.

Ethereal vocals were also part of “Pass the Baby,” the new album’s most complex track. It began as the closest the band has come to trip-hop, only to switch to a prog-metal coda. Positioned about halfway through the show, and performed while the stage was washed with dim blue light, the song was the evening’s niftiest change-up, albeit a cryptic one.

Most of the other tunes mined personal regrets or offered advice to the lovelorn and melancholic. “Honey, you are free/As much as you can stand to be,” counseled one of the new songs. If that message sounds as much a curse as a blessing, it was coming from a band that is currently operating very well within its self-imposed limitations.