The members of Michigan-based quintet Greensky Bluegrass don’t like labels, something they probably should have considered before settling on their moniker in 2000.

“We’ve certainly had to fight with the fact that the word ‘bluegrass’ is in our name,” says dobro player Anders Beck, who joined the group in 2008. “It doesn’t bother us as much as it used to [but] when we were trying to evolve past bluegrass into something else, we were like, ‘Well, do we drop the bluegrass?’ But no, then you lose the pun.”

Instead, Beck says, the band lets the music speak for itself, even if it’s hard to avoid being pigeonholed because “we’ll always play banjos and mandolins.”

It would be fair to classify the group as bluegrass based on its last album, 2011’s “Handguns.” Banjo, mandolin, dobro, acoustic guitar and upright bass make for an unmistakably bluegrass-y sound, as does the twang in the vocals of singers Dave Bruzza and Paul Hoffman. It’s not until one of the record’s last songs, “Bring Out Your Dead,” that Greensky reveals a darker, distorted side, one that’s more blues than bluegrass.

According to Beck, the band’s forthcoming fifth album, “If Sorrows Swim,” will build on the more folksy elements of “Handguns” while continuing to push Greensky past its namesake.

“It’s probably a little more accessible on some levels,” Beck says of the record, which he hopes will be out this spring. “There’s more of a pop sensibility in the writing. … There’s a couple songs … I could hear being on the radio.”

Might the album, then, be a reaction to the pop success of such folk revivalist bands as The Lumineers, Of Monsters and Men, and Mumford & Sons?

“No, we’re not smart enough to do that,” Beck says. “A lot of it has to do with what we’re listening to. … The songwriting was influenced more by Arcade Fire than Bill Monroe.”

You could say a similar thing about the band’s live shows — just substitute the Grateful Dead or Phish for Arcade Fire. Greensky follows in the jam band tradition, varying setlists each night and playing left-of-center covers. During those 15-minute-long jams that crop up, Greensky sounds closer to a rock band. Close your eyes and you may even forget you’re listening to banjos and mandolins.

Even still, “jam band” is another label Beck hesitates to take ownership of.

“The reason why jam bands will get flak sometimes is because if you’re exploring musically every night, there’s a good chance you might fall flat on your face,” Beck says. “We jam onstage because we like to play music. Sometimes you just don’t want the song to end because it’s going somewhere cool.”

Cover This

Greensky Bluegrass is known for its live covers, which span genres. “It’s a way of saying, ‘Hey, we’re all on the same page, we all like good music,’ ” Anders Beck says. Here’s a sample:

“When Doves Cry”: You wouldn’t think this synth-based Prince classic would suit Greensky’s style, “until you hear it as a bluegrass song,” Beck says.

“Atlantic City”: The Bruce Springsteen epic is an example of a more straightforward cover, as the band stays faithful to the original arrangement, adding an extra dose of twang.

9:30 Club, 815 V St. NW; Sat., 7 p.m., $18; 202-265-0930. (U Street)