It features a more diverse instrumental palette than the band's debut album, Skin 'Em Up (1981), but was seen as a departure from the group's original, immediate sound.

Celts and Cobras features more varied instrumentation than previous Shakin' Pyramids releases, but was seen as a departure from the band's original, immediate sound.

[2][3][4] Trouser Press said, "Celts and Cobras offers a higher percentage of their own songs, but on it they're accompanied by piano, accordion, electric bass and even — gack!

"[3] AllMusic gave the album 3/5 stars, and opined that "the energy and verve of their debut had been replaced by a stultifying maturity.

"[1][2] Ethnomusicologist Craig Morrison wrote, "[Celts and Cobras] drifted farther from rockabilly as they broadened their horizons... One writer asked, "From neo-rockabilly to neo-schlock—is this neo-progress?