“I don’t love rock songs so much,” The Frames’ Glen Hansard says over the phone prior to a Tuesday night show in Minneapolis. “I know I should … I’m in a rock band.”

The oddity of that statement is obvious, but in exploring the persona of the Irish-born frontman, such an utterance seems to typify Hansard quite well.

Hansard doesn’t want “over the top.” He doesn’t want “in your face.” He wants understated. He wants subtlety. He wants a connection, both with his music and with his audience. Perhaps that’s why he so enjoys touring in America.

Back in Ireland, The Frames, whose lineup also includes Joe Doyle, Colm Mac Con Iomaire, Rob Bochnik and Johnny Doyle, are revered. Their albums top the charts. Their concerts sell out. On this side of the Atlantic, the band is more of an afterthought in an ever-burgeoning field of British, Scottish and Irish musical imports. And Hansard … he’s sort of fine with that.

“What we have over here I really like,” Hansard says. “I feel like we’re drifting somewhere really interesting.”

Drifting because The Frames don’t receive the radio or video play most premier bands enjoy. Instead their fan following has developed more organically, by word of mouth.

“I think that’s a pretty good way of getting into people’s minds,” Hansard says of the referrals. “We don’t want to sound too self effacing, but it’s great that all the people that come to see us have heard that we’re good.”

And, to grossly understate the matter, they are good, which makes it so surprising the band remains largely off the radar stateside. Tastes don’t vary that much between Ireland and the U.S. So when Billboard labels The Frames as Dublin’s second-biggest band (behind those no-names U2), you would think it would cause more than a subtle ripple across the pond.

But this is how Hansard likes it. He doesn’t want to involve himself in the corporate music dog and pony show. He doesn’t get any satisfaction out of simply being an attraction. And call them selfish or demanding, but Hansard wants to get something back, as indicated in a recent interview with Ireland’s Hot Press magazine. He’s fine with less, because he wants more. He wants a sense of connection.

“The worst feeling in the world,” Hansard says in the piece, “is coming offstage feeling like you’ve just given people what they want and you haven’t had any satisfaction from it. You just feel like you’ve whored yourself.”

That’s why Hansard is not into signing sessions or hocking albums. That’s why he doesn’t use radio play or feature stories in Rolling Stone as a measuring stick for success.

“It’s the old adage, it’s not the destination, but the way of traveling,” Hansard says of how he does define success. “When we’re on tour, it feels like we’re on vacation. We’re not stressing. We’re just being ourselves.”

The intimacy Hansard craves with his audiences is abundantly present on The Frames’ latest album, “The Cost,” which hit American shores in late February. Released in late September in Ireland, the album shot up to No. 2 on the national charts, largely buoyed by the band’s signature honest sound. In this instance, Hansard and Co. have taken that honesty to new heights, recording the album live in just over two weeks with producers Stephen Fitzmaurice and former Frames guitarist David Odlum. No tweaking, no editing, just a take-it-or-leave-it final product.

“There’s a fair criticism that’s been leveled at us over the years that our records don’t match what we do on stage,” Hansard says of the motivation for the live recording method.

As ever, Hansard lulls listeners in with his modest, honest confessions, winning them over with his poignant poetry. Time and again, with tracks like “Rise,” and the sweeping soundscape of “True,” Hansard and his mates draw you in like a moth to a flame, only to light off and leave you seared, and often saddened, after a crushing crescendo.

That pattern ought to be a familiar one to Frames fans, as Hansard readily admits the blueprint was born from the band’s old bag of tricks.

“We call it the wedge,” Hansard says. “It’s just a dynamic that we have naturally. I don’t really know where it came from. The violin tends to make it a little anthemic.”

The end result of the live recording session synchs well with the band’s proclivity for authenticity. Perhaps that is a major reason why publications, like Ireland’s Evening Herald, are labeling “The Cost” the best thing The Frames have ever done.

Praise is great, but now comes the fun part for the band, as they continue their U.S. tour next Thursday at D.C.’s 9:30 Club.

“When you record in the studio, you take away one half of the thing that makes us good, and that’s our audience.”

This is the part where The Frames feel fulfilled. This is the part where they can get something back.

• For more on The Frames, visit www.theframes.ie.

Off Track

A few more thoughts from The Frames’ Glen Hansard …

On his preference between the versions of “Falling Slowly” and “When Your Mind’s Made Up” previously recorded for The Swell Season album and the versions on The Frames’ “The Cost”:

Glen Hansard: I prefer the Swell Season version of both songs. They  [the songs] were younger then. Our version sounds more like Coldplay, which I don’t particularly love.

On critics noting that their recorded work doesn’t match with the band’s charming live shows:

GH: If each song [on the album] had a two-minute introduction it would probably be a more ‘up’ album.

On the contrast between his somewhat gloomy music and his buoyant personality:

GH: Songs are like self medicating. You get all your blues out on the table. Some of the most relaxed people I’ve ever met are punk rockers. They play their asses off and go wild and then go slip into their Birkenstocks and eat their vegan dinner.