Low Cut Connie is a band that basically defies all laws about how a band is supposed to make it in 2013. I know this because instead of sending me a CD or asking me to review a show, the duo's singer took me out to lunch and invited my band to open for them.

Combustible frontman/upright pianist Adam Weiner graduated from the same New Jersey high school as me, five years earlier, and first contacted me on Twitter because I'm a music critic from his hometown of Cherry Hill. I'd heard his band because I'll check out anything “Dean of Rock Critics” Robert Christgau grades an A- or higher, and their bawdy album called Get Out the Lotion stands out for other reasons.

Weiner shares songwriting duties with drummer/guitarist Dan Finnemore, whose own ditties like “Darlin'” and “Brand New Cadillac” are raucously juiced with American rockabilly. Weiner's twisted anthems like “Big Thighs, NJ” and “Shit, Shower and Shave” earned them the “scuzzball” descriptor (from Christgau) and the term was subsequently (and proudly) passed around in their press milleu. But the band is great on a ballad like “Full of Joy” even when they deviate from the loose-rocking schtick. I would've been a fan from that alone, but becoming friends with them has been a whole other fascinating rabbit hole.

For example, if I had not known these guys, I never would've found out that Merrill Garbus of tUnE-yArDs was a camp counselor with Weiner at Appel Farm, or that she played Prince and Michael Jackson songs at his wedding, well after winning the Village Voice Pazz & Jop critics poll for her second album w h o k i l l. The pompadoured Weiner's a strangely connected guy, and a great salesman, which is why his band has one of the most quixotic success stories in recent memory.

Their two albums are great–I didn't even realize my Weekly editor Ben Westhoff knew they existed until I saw that he listed them in his top ten last year. Their ferocious live show, complete with instrument-switching and Weiner leaping atop his bench to pound the keys, is probably unmatched in all of rock right now, at least until Gogol Bordello comes back around. Every time my bassist sees Low Cut Connie, he vows to steal their stage moves. They upstaged the Shins during a recent Third Man Records opening gig and allegedly made a fan of Jack White in the process.

NPR calls them “The Self Deprecating Bar Band,” a title that fits squarely with songs like “(No More) Wet T-Shirt Contests,” in which Weiner mock-threatens that his Christian phase is coming soon. Rolling Stone has endorsed the band as well, with two 3 ½ star reviews for two self-released albums. Their song “Boozophilia,” ended up in the magazine's top 50 songs of 2012.

The video for it was filmed at Philly's North Star Bar, on a night when my band Dan Ex Machina opened for them. In the clip, we can be clearly seen dancing shirtless in the audience. It was a great show, and in the dressing room between sets I had the pleasure of watching a semi-shitfaced Weiner take a piss in the corner. (When I recall this, he tells me the story of a voice coach who made him press down on her bladder as hard as he could with his hand as she demonstrated how to sing through the uh, pee-pain.)

Sounding like Jerry Lee Lewis and Screamin' Jay Hawkins is both a blessing and a curse for the band, who I'd call a healthy anachronism and could break wide open from say, having one of their tunes selected to accompany the right sleazy moment in True Blood. Weiner sums up their current obstacle:

“We had a gig at Joe's Pub, a swanky, upscale, seated dinner place in Manhattan. “The week before us, Leonard Cohen did his press junket there. Elvis Costello has been there. Before that we were playing little divey bars. We went out and played one of the best shows we've ever done. We ripped it up, we blew up that room. That night there was an agent from a particularly large booking agency there to see us destroy a major venue in New York City. He spoke with our lawyer the next day and said, 'You know, they're really amazing. But I have no idea what I would do with them. Pass.

Weeks later we played in Philly. This band I won't name played first, to about five people. They had like, three laptops onstage, had their eyes closed, staring at their shoes. Nothing going on in that room, onstage or in the crowd. That schmuck from the booking agency came down that night, from Brooklyn to Philly, in a rainstorm, to see this band and proceeded to sign them. You tell me what he saw in that band, at that show.”

Weiner insists the band “skipped steps,” and while they're grateful of the position they're in, they missed the grassroots buildup, the Best New Music, the festival circuit. They're shopping demos of a potential third record to labels, as the demands of being their own record company is threatening to take over the time they use to make music. When I ask Weiner his ideal next step, he answers with something that no Pitchfork darling would ever say, or maybe something no band would ever tell an interviewer that they're not friends with: “We want,” he says, “to be on TV.”

It's true though, that their leather-jacketed antics and physical feats onstage win people over just as much as their songs do. They've made converts of people like me who don't tolerate “nostalgia” acts or long for a throwback. But for a rock and roll band that fits neither Nickelback's nor Arcade Fire's profile, that's still an uphill climb. Once people are watching, Low Cut Connie's show speaks for itself. They're clever (and good) enough to get to wherever they want to be. Even TV.

Low Cut Connie plays the Hotel Café on Saturday, March 23, and the Echo on Monday, March 25.

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