May Fire’s “You Make It Right” starts off with some fuzzy guitar and singer-guitarist-keyboardist Cat Tasso singing a simple melody through a distorted microphone. She sounds like a drunk and surly Kim Deal, in a good way. Drums, bass, and new-wave keyboards kick in, and a second fuzzy guitar starts lurching around like a menacing shadow in an alley. At the chorus, Tasso’s voice sobers up and hits the high notes without ever losing the badass edge that she had at the beginning of the song.

If “You Make It Right” had come out in 1994, it would have been a big radio hit, and deservedly so. May Fire would be stealing the show at Lollapalooza, the major labels would come courting, and MTV would be all over them. Instead, it came out in 2007. The band is playing the Beauty Bar, is two-thirds of the way through self-releasing a “trilogy” of EPs, and has some charming videos on YouTube.

But, hey, this decade’s marks of success are more interesting than those of the ’90s in a lot of ways. For instance, May Fire’s “Marcha” was iTunes Latino’s single of the week last fall. We didn’t have iTunes in 1994, and there wasn’t a whole lot of rock en español in the English-speaking world back then either. Tasso is Chilean and two of her three bandmates are Colombian, but most of their songs are in English. Tasso recently told Guitar Player magazine that her music is influenced by Spanish boleros. That may be a stretch, but I’ll take it as a sign of interesting things ahead for the band.

MAY FIRE, Beauty Bar, Thursday, April 3, 8 p.m. 619-516-4746.