Like Funeral Dress II, Strawberry was released in 2011, and helped spur long-standing "dean of rock critics" Robert Christgau to declare Wussy "the best band in America."
"Although it was Lisa's idea to basically set ["Funeral Dress"] to the tune of 'Teenage Kicks,' " the New Wave power-pop classic by Northern Ireland's the Undertones.
"My daughter had a friend who got killed, and she said to me, 'I gotta go out and get a funeral dress,' " recalls Cleaver, 53. That sparked the songwriter to pen the carpe diem chorus in which Walker's dulcet voice crackles while being shadowed by Cleaver's high-pitched quaver: "You're alive, each and every day you're alive / Counting every second you're alive, knowing it'll never come again."
"We don't really write cheery," Cleaver says with a laugh. "Though I don't really consider the stuff that I write as dire as everybody else does. My kindergarten picture pretty much sets me up for life. I'm sitting there like I just watched my puppy get hit in the road. That's just who I am."
Cleaver, who formerly fronted the rock outfit Ass Ponys, which flirted with mainstream success with the 1994 MTV hit "Little Bastard," grew up in a farming community north of Cincinnati. He was the son of a factory-worker father whose musical tastes ran to Afrobeat star Manu Dibango and Jamaican duo Dave and Ansel Collins.
"He liked a lot of weird stuff that always surprised me," the son recalls. "He'd dance around the house in his underwear."
"The first album I ever bought was Tommy James & the Shondells' Crimson & Clover," Cleaver says. From there, he schooled himself on sharp-eyed writers such as Ray Davies, Pete Townshend, and John Prine, as well as David Forman, Dirk Hamilton, and other more obscure faves.
In the 1980s, he formed Ass Ponys, a band specializing in portraits of small-town oddballs and tough-luck losers, in songs like "Gypped" and "Peanut '93" on the band's 1994 major-label debut, Electric Rock Music.
That gave Cleaver, who describes himself as "a hillbilly dinosaur - I only switched from a rope belt about a year ago," a taste of success, and his first-ever plane ride at age 35, when the A&M label flew the band to Los Angeles.
Ass Ponys peaked, in Cleaver's estimation, with their 2001 album, Lohio. Around that time, he met Walker, who's 18 years younger. "There's a big age gap, but we're kindred spirits," he says of Walker, who, like him, "grew up in the middle of nowhere," in her case outside of Muncie, Ind.
With his former band, "I was never that keen on being a front person. Early on, we tried out people to sing because all I really wanted to do was write the songs and play rhythm guitar and not have to worry about it.
"With Lisa," Cleaver continues, "it just makes it easier. Very obviously, she's just far and away a much better singer than I am. It's nice. I think we reach a lot wider audience this way. . . . With two writers and two singers and everyone in the band sings, we just have a lot wider range of things we can do."
The Wussy name was Cleaver's idea: "I just like the way it looks on a T-shirt. It's another one of my names ensured not to get anywhere."
Walker and Cleaver's voices have a sweet and tart blend, a deeply satisfying female-male mix that, along with their roots-rock proclivities, puts them in a country-tinged continuum that includes Gram Parsons and Emmylou Harris, and X's John Doe and Exene Cervenka.
Cleaver and Walker were together first musically and then also romantically, but haven't been a couple for more than six years now, and each is in a relationship with a new partner. When a man and woman sing about shattered love together, however, listeners tend to interpret it as ongoing autobiographical drama.
"People think that songwriters can't have artistic license," Cleaver says. "It is coming from you, but it's not necessarily your experience. Stephen King isn't a swamp monster, he just writes about them."
Though the band has been productive over the last half-decade, Wussy isn't so easy to keep up with. They record for the indie Shake It label, based in a Cincinnati record shop. Due in part to day jobs - Walker's a waitress, and Cleaver worked as a stonemason for the last 15 years before giving it up on the advice of his chiropractor - they haven't toured much.
"We have never been very good at the game," Cleaver says. "We're playing it the best way we know how. . . . But we're touring more this year than we ever have before. We're going for it."
This run of shows pairs Wussy with rising Philadelphia rockabilly-plus band Low Cut Connie on Friday at the North Star, and on Saturday at the Mercury Lounge in New York. The two songwriters will also do two weeks in the United Kingdom, in Cleaver's first-ever trip abroad.
A career-spanning best-of Wussy collection called Buckeye has also just been issued on the British label Damnably, and can be heard in the United States on streaming music services such as Spotify.
Being praised as the best band in the land by Christgau has been useful, Cleaver says.
"It's like in Napoleon Dynamite when he says, 'This is the worst video ever made,' and his brother says, 'How could you possibly know that?' " says Cleaver, impressively mimicking actor Jon Heder. "It's the same thing with this. . . . Compared to what? But we were very surprised and obviously very flattered. He's been very helpful. . . .
"We've always been kind of a critic's band. Ass Ponys were, too. I've always considered it a fortunate thing. I'd like to appeal to more people. It would be good to make even a partial living at this."
Contact Dan DeLuca at 215-854-5628 or firstname.lastname@example.org, or follow on Twitter @delucadan. Read his blog, "In the Mix," at www.philly.com/inthemix.