Luscious Jackson, the band, named after ’60s Philadelphia 76er Lucius Jackson, the basketball player, doesn’t fit neatly into one musical genre, a problem that plagues many musical artists trying to push the envelope.

Unless, of course, there’s a genre that lead singer Jill Cunniff calls “upbeat grooves that inspire you to get your butt off the couch and clean the house.” Bass-driven hip-hop-rock crossover might be a little more specific.

Luscious Jackson is Gabby Glaser, guitar and vocals, Jill Cunniff, lead vocals and bass, and Kate Schellenbach on drums, successfully combining a soft-rap style, R&B groove with the lyricism and fun of pop.

How Luscious Jackson formed their uber-cool, ultra-downtown style is well documented. Cunniff, Glaser and Schellenbach met as teen-agers on the underground music scene of the late ’70s-early ’80s downtown New York City, bonding with a mutual appreciation of Bad Brains, ESG and the Slits.

The friendship became musical collaboration when Cunniff and Glaser pooled tip money to create the first Luscious Jackson demo in 1991, which they brought to friends the Beastie Boys.

In 1992, Luscious Jackson’s demo was combined with three new songs to become “In Search of Manny” released on the Beastie Boys’ Grand Royal label. Nineteen ninety-four saw the release of the band’s “Natural Ingredients” featuring “City Song” and “Here,” a track later chosen as the first single and video from the “Clueless” movie soundtrack. In 1996, the album “Fever In Fever Out” hit the streets, producing a Top 40 hit with the inescapable “Naked Eye” of the summer of 1997.

The band also enjoyed success with its hip commercial for the Gap later that year, an ad readers of TV Guide voted the best in the campaign. But don’t mistake them for a commercial band — despite having been written up in almost every prestigious publication around and having had a pop hit, they maintain a low profile.

Though they make a point of saying that their music is definitely not politically oriented, they do a considerable amount of work for charities. From their involvement in Red Hot ‘n Rhapsody for AIDS research to the Tibet Freedom Concert to visibly supporting the pro-choice cause, it’s obvious that Luscious Jackson cares about the world going on around them.

Glaser has a lot to say about Mayor Rudolph Giuliani’s impact on New York City. “He’s cracked down on crime, and that’s certainly good, but he’s very extreme. He wants to close down important programs like centers for the mentally disabled and children, in addition to having a negative impact on the arts scene, like that whole thing with the Brooklyn Museum.”

She describes the mallification of New York as being “like a cancer that spreads. Seeing chain stores and things that all look the same make the tourists feel more comfortable, but it’s taking the life out of the town.”

Luscious Jackson had a great time playing Lilith Fair last summer, despite the cynical press the tour got. “It was really misrepresented in the press. There were a lot of guys there, and all the girls didn’t have hairy underarms,” Glaser said. “It was about a bunch of musicians jamming out.”

Among the highlights of the tour for Glaser was being able to perform with Bonnie Raitt, Chrissie Hynde (“she’s a WILD woman”) and Sheryl Crow (“she put in an amazing show — she’s an amazing musician”).

Last year, Luscious Jackson released its most mature, radio-friendly album to date, called “Electric Honey.” From made-for-dance-floor tracks like “Nervous Breakthrough” the opening track, to smooth-as-silk songs like “Ladyfingers” and “Sexy Hypnotist,” “Electric Honey” shows that they know how to create hip, fun party music while maintaining their downtown style.

“Electric Honey” is full of the clever hooks and catchy tunes that made “Naked Eye” from their last album “Fever In Fever Out” the summer hit of 1997. Singable lyrics like “Thanks to you/I had a nervous breakthrough” and “I’m a sexy hypnotist/lost on the strip/and I’ll bear it all/’cause abs and buns are so much fun” abound, as do the loud, chunky dance beats that drive the CD’s groove.

The most exciting revelation that comes from “Electric Honey” is the idea that the band is not being corrupted by its growing celebrity — Luscious Jackson’s sound is evolving without losing its roots.

Each album simply sounds better, like more money is being put into the production and the same feeling that exists on “In Search of Manny” is still here. In short, it’s the same cool, party-ready friend you’ve always known but instead of wearing dime-store vintage clothes, she’s got fancy new duds.

Luscious Jackson will perform with Smash Mouth on Friday, Feb. 25, at Boston’s Orpheum. For information, see www.lusciousjackson.com.