Washing up on U.S. shores at roughly the same time as fellow pop classicists Elvis Costello and XTC, Squeeze never enjoyed the commercial success in the States that had greeted the previous generation of British Invaders a decade or so before. But back in the day, Chris Difford and Glenn Tilbrook were frequently looked upon as the Lennon-McCartney of their generation, packing Squeeze albums with literate pop gems as timeless as “Take Me I’m Yours,” “Goodbye Girl,” “Cool for Cats” and their eventual U.S. breakthrough, “Tempted.”

Difford recalls the uphill battle they faced in the States.

“When we arrived in America, we turned on the radio and it was ‘Baker Street’ and REO Speedwagon and Styx and Zeppelin. Not that there’s anything wrong with hearing Zeppelin, obviously. But that was the bulk of radio. It did change, though. College radio became huge, and we managed to sort of wing our way through college radio and do lots and lots of U.S. tours.”

Reminded that he and his songwriter partner were seen as a lesser-paid version of Lennon-McCartney in those days, Difford responds with brilliant self-effacing British wit that when he heard that kind of talk, “I was thrilled, although I didn’t know which one I was.”

Because of when their early albums hit the streets (and possibly the fact that they were fairly young and British), they were seen, like Costello, as part of the New Wave revolution, a tag they’ve spoken out against on more than one occasion.

“Looking back on it, what does it matter?” Difford says. “A label is a label. For a long while on American radio, it was difficult to say, ‘Well, what is Squeeze? They sound like the Beatles. They sound like New Wave. But they’re not either of those.’ So it was frustrating, I guess, for people who were programming radio stations. We definitely weren’t punks, but people sometimes said we were, which I found quite interesting.”

Their self-titled debut, retitled “U.K. Squeeze” in the States, was produced by an artist whose music proved a crucial inspiration of the New Wave era, John Cale of the Velvet Underground.

“I’ve become a huge fan of it, oddly enough,” Difford says of the 1978 release. “I went through a period of thinking, ‘It’s too far back for me to have any emotional attachment to that.’ And also I thought it was a bit scruffy. It was a production by John Cale, which was amazing. But it wasn’t really Squeeze as I knew it. It was quite a bizarre mixture of tracks. But now I look back on it with new eyes in some ways. I think ‘Wow, that’s amazing. Here’s a bunch of young kids making their first album and having such a great time.’ ”

The band’s second album, “Cool for Cats,” was even better, but they really hit their stride with 1980′s “Argybargy,” which gave the world “Pulling Mussels (From a Shell),” returning the following year with “East Side Story” and the single “Tempted.”

Difford sizes up that early burst of creativity three decades later.

” ‘East Side Story’ was probably the pinnacle of our holding hands as songwriters, if you like. That was a pretty terrific time, and we had a fantastic guide in Elvis Costello. Then, I think we got lost a bit. We were tired from touring, and we were all over the place. But then, I think it came back again for a while when we made the ‘Some Fantastic Place’ album,” released in 1993.”

Hold on. Does this mean Difford dismisses 1982′s “Sweets from a Stranger” album, with such songs as “When the Hangover Strikes” and “Black Coffee in Bed”?

“I like a couple tracks on that,” he responds. “But overall, I think it’s quite dark. It was right before we split up for the first time.”

“Black Coffee in Bed” gave Squeeze their second minor U.S. chart hit, followed that same year by “Annie Get Your Gun” and 1985′s “Hits of the Year.” But it was 1987 by the time they went Top 40 on the Hot 100 with a song called “Hourglass,” a breakthrough Difford says had more to do with MTV than anything.

“We made a fantastic video,” he says. “And it was getting played constantly in rotation on MTV and VH1. So there was a lot going on, and it sort of helped steamroll the track onto radio.”

A second Top 40 hit, “853-5937,” was pulled from that same album, 1987′s “Babylon and On.” And they’ve managed a handful of modern-rock radio hits since then. But Squeeze’s biggest-selling album here remains the early ’80s greatest-hits collection, “Singles — 45′s and Under.”

It could be argued that the album is a pretty decent advertisement for the live show, but Difford believes the upcoming “Live at the Fillmore” does the best job of that.

“I think the live album is much more a testament to this band,” he says. “… It’s just a very strong representation of Squeeze as it is today.”

Their last album of newly written material is “Domino,” which hit the streets in 1998.

“It was at the end of a run of really good recordings,” Difford says of “Domino.” “And I think we just got tired, or I got tired anyways, of the constant touring. I wasn’t concentrating. I took my eye off it, really. And I don’t think I was giving it my all.”

Asked if there’s any hope of new material emerging, Difford says, “We talked about it at the beginning of the year, but we’ve not really found that spark. …

“When you’re younger and you’re in a band and you have to make a record by September or something, you knuckle down and you make records. In this day and age, it seems to me like there’s no urgency because the record industry doesn’t exist for a band like Squeeze anymore, so you don’t stay up all night thinking, ‘I’ve got to write another song for tomorrow,’ because you don’t know what you’re chasing.”

Reach the reporter at ed.masley@arizonarepublic .com or 602-444-4495.