Los Amigos Invisibles was discovered by accident. Their story begins in Venezuela in 1991. There they found a hometown audience still hungry for ’80s American disco, complete with glittery synth blasts, ubiquitous slap bass, and four-on-the-floor mentality. But the commercial dance club scene in Caracas was all but dead at the time, so LAI made cultural inroads by hosting underground dance parties.

By 1995 they had recorded their debut, A Typical and Autoctonal Venezuelan Dance Band. They took 20 copies with them on tour to New York and convinced a record-shop owner to give them rack space. Fates converged when David Byrne bought a copy and dialed the phone number on the back of the CD. LAI was without contract and were free to deal. Byrne signed them to his boutique world-music label Luaka Bop and released three of their nine CDs.

Critics tag Los Amigos Invisibles with lofty descriptors such as alt funk and acid jazz, but I’ve never believed the band to be more than an excellent parody of the time when Donna Summer and the like were topping international dance charts. “It’s not the way you wear your dress,” Julio Briceño sings, “you should be wearing a whole lot less.” LAI also parodies itself. In “Masturbation Session”: “I’m dying to tell you what I think about you/ My blanket is not cool, because the TV is turned on.” (Possibly some of the song’s comic nuance is lost in the Google translation, but you get the idea.) “Porno Song” samples the crassest of orgasmic moments from 1970s porn-video soundtracks and loops them with breathy lyrics and that thud-thud-thud kick beat into a pop architecture that both celebrates its roots and laughs at itself.

Bostich + Fussible also performs.

LOS AMIGOS INVISIBLES: House of Blues, Tuesday, September 6, 7 p.m. 619-299-2583. $20, $35.