It’s hard to believe that Maná, the enormously popular Mexican rock band, has been together since 1986, give or take a few lineup changes. Its show at Madison Square Garden on Wednesday — one of two, both sold out — seemed more like the work of a band recently convened by supermanagers in order to be attached to advertising. The four handsome core members didn’t evince much chemistry, no inside jokes; they hardly interacted. The show was tight as a drum, stripped of longeurs and entertaining, in a businesslike way.

On the other hand ’86 is about right. That explains — has always explained — Maná’s sound in relation to the reggae-rock of the Police, from which this band drew heavily. (To be fair, in recent years this influence has waned: Fher Olvera’s voice has thickened, and on the band’s new record, “Amar es Combatir” — “To Love Is to Fight” — from Warner Music Latina, he doesn’t sing high notes á la Sting anymore.) It also explained the sudden onset of hair-metal guitar solos in the show’s second half, as well as the midconcert, set-piece drum solo by Alex González, the band’s one clear virtuoso.

Much respect to this solo, which was a blizzard of speed and technique, and a maze of neat rolls and tiny accents across a huge kit. (Mr. Gonzalez and his drums were on a motorized riser, which turned 90 degrees in each direction, to prove that his limbs were doing what you thought they were doing.) He smiled through it all, played the snare drum behind his back for a while and finished by standing up and keeping his rhythms steady. Then he stood atop the stool and jumped off it, triumphant. There was no second-guessing in his work. He was driving the disciplined, optimistic kapow! of ’80s pop right into the heart of the present-day culture, and the middle-aged Latin American audience knew its coordinates cold.

A lot of Spanish-language rock has never lost that authentic optimism. In Maná’s songs the hope and romance in old songs like “Vivir Sin Aire” (To Live Without Air”) or new songs like “Manda una Señal” (“Send Me a Signal”) and “Combatiente” (“Combatant”) is authentic even when the sonic material isn’t. Mana is a loud rock band with a lot of female fans; it’s on the side of safety, dreams, love and comfort. And likewise the music: Whether the template is the Police, U2, or broad-gesture ’80s pop-rock like Journey, you hear each chord change nosing confidently around the corner.

In “Se Me Olvido Otra Vez” (“I Forget Myself Again”) and “Perdido en un Barco” (“Lost in a Boat”), run together as a medley, the band played mock salsa, stretching its musicianship a little. In its cover of the old Mexican ranchera “El Rey” (“The King”), the group switched from a ranchera two-beat to reggae-rock, then to a straight four-four new-wave; in the new song “Bendita tu Luz” (“You’re Blessed With Light”) it played a modified version of Dominican bachata. These were high points. Maná’s music stretches pretty thin when it doesn’t look further back than the ’80s for cultural input. But when it did, the concert lit up.