In 1993, an American man who was not yet 30 broke the hearts of music lovers around the world when he broke up his band. That man, Charles Thompson (aka Black Francis) and three accomplices created four rock albums over seven years. The Pixies found themselves in a strange position in the alternative-rock world: influential, groundbreaking — and beloved.

It took Frank Black, the name Thompson used in his solo career, more than a decade to reunite his band. Kim Deal, a Pixies cofounder whose musical career has flourished on her own as well, returned to the fold, with her bright smile concealing her drug problems, not to mention the band’s extra kilograms and thinning hair.

It was one of the most successful revivals in rock history. Back on the road, the Pixies made more money between 2004 and 2013 than they had during their first incarnation. Then, on June 4, 2013, Deal left the group. It was traumatic, even if not as crushing as the breakup a decade before.

How could anyone even think of, much less listen to, the Pixies without her? As it turned out, it was possible, even if your heart was broken. Broken not necessarily due to Deal’s absence, but because the Pixies’ music is moving, painful and joyous all at once. That’s the way it was Tuesday night at Jaffa’s Bloomfield Stadium.

Do you remember the first time you heard “Bone Machine, the first track on “Surfer Rosa,” the first full-length Pixies LP? It was the first song of the band's concert in Israel, a bombardment heralding things to come.

The Pixies hit their audience without mercy and without a break between songs. The pace was worthy of the group’s reputation as the fastest slow band in the world, turning moving ballads into an echoing shriek fest.

The Pixies have plenty of songs two minutes long, so dozens can be crammed into an hour. That’s exactly what they did for two hours. Voltage drops were few and far between. Jazz great Sun Ra said about Black Francis when they were playing festivals 25 years ago: “Boy, you sure can scream.” On Tuesday, Francis sang higher than usual (on “Greens and Blues” he sounded like Deal) and more hoarsely, but in the rare moments of tenderness he proved he’s not only a legendary screamer, he’s a good singer.

David Lovering, whose drum sounds could destroy militias in Iraq, broke hearts on “La La Love You.” Guitarist Joey Santiago — I bet you didn’t know he composes music for TV series including “Weeds” — began nearly every song with distortion that could be set to a symphony.

And Paz Lenchantin maintained Deal’s tradition of a steady, unornamented bass line. Even when she strayed beyond Deal’s vocal range in “Where Is My Mind,” it was hard to detect any anger against her because Black Francis was persuasive in his call to repent (in “Caribou”).

The Pixies did a few songs from their new album “Indie Cindy” and a couple each from “Trompe le Monde” and “Bossanova.” They stuffed the concert with tunes from the wonderful “Surfer Rosa” and “Doolittle” — and not only the most famous. Precisely on songs like “Cactus,” “River Euphrates,” “Ed Is Dead” and “No. 13 Baby” — the last is about a woman six feet tall with a “tattooed tit” — the emotional levels peaked. Pulses raced to the ‘90s and back without hesitating.

They turned in an exacting performance of “Here Comes Your Man” and “Monkey Gone to Heaven,” and for an encore came “Gouge Away,” a song that contains the Pixies’ entire philosophy in a nutshell: how to play the chorus first, shift into overdrive for the verse and, before the climax, return to the chill chorus. They know how to sing about a Bible story without sounding like hicks, how a simple bass line can have such an unorthodox structure, and how a primal roar can touch the heart like a lullaby.