It's been a decade since the release of the Walkmen's debut album, "Everyone Who Pretended to Like Me Is Gone," but the New York rock band very nearly didn't make it to the 10-year anniversary party. Singer/guitarist Hamilton Leithauser says now that the group, releasing its seventh album, "Heaven," on May 29 through Fat Possum Records, almost disbanded numerous times.

"We went through a phase of not caring and put out some pretty bad stuff," Leithauser says, pointing to a time in the band's career before 2008's "You & Me." "We had a rethinking moment where we said, 'It's inexcusable that we're putting out stuff we're not proud of.' There's no point in doing this if you're not proud of it." He adds, "Since then, we've liked all the music we've done. There's been a lot more creative output."

In particular, Leithauser is talking about "Heaven," which the band-Leithauser, drummer Matt Barrick, multi-instrumentalist Pete Bauer, guitarist Paul Maroon and bassist Walter Martin-recorded during two sessions in and around Seattle with producer Phil Ek. The musicians were looking for more direction than achieved on their last disc, Lisbon, which landed at No. 27 on the Billboard 200 in September 2010 and has sold 51,000 copies, according to Nielsen SoundScan. Leithauser calls that album the product of "endless attempts that no one will ever hear." It also marked a period of reorganization for the band, its initial disc for Fat Possum and the first release under the guidance of Mick Management.

Fat Possum marketing manager Justin McGuirk says, "A label can only do so much for a band in that process, so we were pushing them to meet with Phil early on. We trusted them a little bit more [on "Heaven"]. They knew themselves, they got in there with the producer, and we just left it up to them to see what they came back with, trusting the product would be good."

In many ways, the album marks a strong leap forward for the group, building off the momentum of "Lisbon." The singles from that previous disc, "Stranded" and "Angela Surf City," were pushed only to noncommercial radio stations, but McGuirk says the plan this time is to urge the Walkmen further into the mainstream. The campaign launched with the first single/title track, a raucous number that sheds much of the band's former indie-rock disaffection. The marketing plan, which involves three forthcoming music videos along with appearances on "Late Night With Jimmy Fallon" and "Late Show With David Letterman," centers on the hope that "Heaven" will finally make the Walkmen a household name-or, at least, get the band's songs heard in more houses than before.

McGuirk says, "This is really going to be the one that's going to help substantiate them and make some of those leaps. I'm not pretending it's going to be a gold record or something like that. Really, I don't like to aim for bold targets like that, but I do think we can get these guys to the 100,000 range on this."

Musically, the band feels that sensation as well. "It's a lot richer, a lot more complicated, and I like the sound a lot more," Leithauser says. "I have no problem with 'Lisbon,' but it's a little one-dimensional-which was sort of the point when we did it. You'd like to outdo your last effort. Creatively, I'm pretty confident that we did . . . We all agree on that, actually, so that's good for us. But it's always nice when other people like your stuff."