For all the hoopla about rockabilly throwbacks The Stray Cats celebrating their 4oth anniversary this year, the stage setup at the Greek Theatre is quite sparse. There’s a lit up logo alongside the band’s name behind them, and two metal trash cans on either side. And then there’s the three guys; Brian Setzer looking more and more like Paul McCartney in a blonde wig as he ages, the wiry, manic energy of drummer Slim Jim Phantom, and the near-rubber Lee Rocker.

See, when a band is this good, with a back catalog this strong, characters this charismatic, they are the show. There’s no real need for fireworks and pyro, because that all comes out in the music.

Following a fun set from the Eagles of Death Metal (with Josh Homme on the drum stool), it obviously didn’t take long to set up for the Cats. But still, when that classic cat logo lit up, the packed Greek went wild. It was a good night for people watching too; the rockabilly clothes and ’50s hair were out in force, and they all had the dance moves to match. A Stray Cats show is a party.

Setzer said from the stage that the band hadn’t played L.A. for 20 years which doesn’t sound right but is in fact true — they played Fullerton in 2003, but the last L.A. gig was at the now-gone House of Blues, West Hollywood, in 1998. So this show really is a rarity, and the band is also celebrating the release of the new studio album, 40, their 10th.

They open with one of those new tunes, “Cat Fight (Over a Dog Like Me),” and play a few more — “Rock it Off,” “When Nothing’s Going Right,” and “Mean Pickin’ Mama.” The beauty of this band is, even their new songs sound old. That’s always been by design. So those brand new tracks fit right into the set with ease.

Of course everyone wants to hear their favorites, and they get them. “Stray Cat Strut” is as cool and undeniably fun as it ever was, while “Gene and Eddie” is still a fitting tribute to the two guys responsible for popularizing this music (Gene Vincent and Eddie Cochran), “Fishnet Stockings” is a lusty romp and “Rock This Town” is pure gold.

Setzer promises us that it won’t be 20 years before we see The Stray Cats in L.A. again and, after this showing, we can only hope he’s right.