For a while, during the mid-1990s, the Mexican rock band Cafй Tacuba looked as if it was heading toward a careful balance of past-meets-future, mixing up Mexican folk and bolero roots with progressive, futuristic, pan-national ideas about rock or electronic music. But even that balance ended up as a limitation; it seems the band would rather work without any expectations at all.

Cafй Tacuba’s new record, “Sino” (Universal Latino), sounds more like classic-rock radio, as did the band’s show at the Hammerstein Ballroom on Tuesday night. And the band’s lyrics, paradoxically, are leaning toward a punk’s general suspicion of categories.

“You define rock or electronica, reggaetуn or hip-hop, on what the radio imposes,” the band’s short, animated singer Rubйn Albarrбn sneered in the new song “De Acuerdo.” “Let’s agree to disagree.” And on “El Outsider” he took the position of living outside of the system: of laws, doctors, the media. In a mock-serious ritual, or a serious mock ritual, Mr. Albarrбn changes his name every album; for now it’s the Aztec-sounding Ixxi Xoo.

He played the first half of the show with a black bowler pulled down over his ears, with eye-slits above the hatband. His singing veers between a beautiful falsetto and an ugly rasp. Punks never had this much fun. It’s not clear how far to trust a proclamation in a Cafй Tacuba song. The band turns sarcasm inside out, showing the sentiment involved in every act of parody. More and more it plays thoughtfully with pop of the 1960s, ’70s and ’80s.