Over the decades, many Beatles-tribute acts have come down the pike — Beatlemania, 1964 and Rain being three of the most prominent.

But The Fab Faux are unlike those acts on a few levels. For starters, they don’t “dress up” like the Beatles — they eschew the vintage early-1960s suits, the psychedelic "Sgt. Peppers"-era uniforms, and the wigs. And the group’s emphasis is on latter-period Beatles songs — from the albums the Beatles made after they quit touring, and which the Beatles themselves never performed live.

And a lot of those songs relied heavily on experimental studio effects, “backward tapes” and painstakingly crafted sound collages. Which makes it even more of a challenge to recreate them onstage. So when The Fab Faux perform, they bring along other musicians — like the Cream Tangerine Strings and the four-piece Hogshead Horns — to help them meticulously reproduce those intricate, latter-period studio orchestrations.

So, The Fab Faux, who formed in 1998, are the most musically ambitious — and accomplished — of the all of the Beatles tribute bands from the last 30-odd years.

And the Faux have a rep for doing shows where they choose one Beatles album and play it in its entirety, then add in some selected tracks from other albums. When the Faux come to the Michigan Theater on Saturday, they’ll perform all of “Abbey Road,” plus other selected Beatles songs.

“Yeah, we don’t do the full-album shows as a rule, but it’s true that it’s what we’ve become known for,” says Faux bassist Will Lee, who is best known for being the bass player in David Letterman’s late-night "house band" for almost 30 years.

“Actually, my favorite kind of shows are the ones where each tune is a surprise to the audience, where it’s kind of like a roller-coaster ride, going back and forth between their eras — it’s sort of like a history lesson,” says Lee by phone from New York City, a couple of hours before heading down to the Ed Sullivan theater for that night’s Letterman show.

“But the full-album shows are cool, too. Audiences who want to know what to expect like those shows, and it’s good way to package a show.”

The Faux also includes Jimmy Vivino, who was music director/guitarist for “The Tonight Show with Conan O’Brien”; drummer/producer Rich Pagano (who’s played with Rosanne Cash, Patti Smith and Ray Davies, among others); guitarist Frank Agnello (Marshall Crenshaw, Phoebe Snow) and keyboardist/guitarist Jack Petruzzelli (Rufus Wainwright, Patti Smith, Joan Osborne Band.). The five members trade off on lead vocals, depending on the song, and all are accomplished multi-instrumentalists. (Lee, for example, also plays guitar, drums and keyboards in the Faux.)

“Our goal is to bring the recordings to the stage, so we focus on that, instead of ‘pretending’ to be the Beatles — it’s hard enough to just be ourselves,” quips Lee. “I was always fascinated by those recordings, and was lucky enough to find four other like-minded guys who believed that this music deserves to be done properly, and as faithfully as possible. Because, this is our classical music.

“Not that this is a stiff performance, by any mans. But the reverence with which we play this material is a reflection of how great those records were.”

Lee and the other Faux members enjoy the challenge of re-producing multi-layered studio tracks that the Beatles knew they would never be called upon to perform live, since they’d quit touring in 1966. “It’s fun, for example, to assemble all of the sounds you hear on ‘Revolution # 9’ — to gather those sound pieces together, and trigger them properly, and decide who’s going to do what,” says Lee.

When asked if there are any Beatles studio tracks that were so reliant on studio effects or trickery that the Faux cannot play them live, Lee replies: “No, there’s nothing of theirs that we can’t do. I don’t say that to be cocky, but we didn’t just walk onstage and start hitting it — we’ve been at this for 13 years, and we’ve learned a lot over the years.”

The group also likes to dig deep into the Fabs’ catalogue and come up with some lesser-known Beatles songs — “crazy stuff like ‘You Know My Name (Look Up the Number),’” says Lee.

Among Lee’s favorite songs to sing are “”Fool on the Hill,” “She’s Leaving Home,” “Here Comes the Sun,” “Girl,” and “I’m a Loser” — “because I am a loser, says Lee, cracking wise again.

As for his day job, Lee says he’s had a blast playing with so many musical greats on the Letterman show for almost three decades. During the show’s first nine-year incarnation, on NBC, the policy was that the house band would be the backing band for that night’s musical guest. “So we had a great time backing people like James Brown, way back in ’82, and Sly Stone, and Difford and Tilbrook from Squeeze……”

Plus, Ringo Starr sat in with the band a few times, recalls Lee.

And even in more recent years, the band backed special duet performances by the likes of Mark Knopfler and Emmylou Harris (on “This is Us”), and John Hiatt and Lyle Lovett (on “Thing Called Love.”)

As a longtime Letterman aficionado, I couldn’t resist asking Lee about what I think is one of the funniest recurring bits on the show: Letterman will do a joke about Dick Cheney, cueing Paul Shaffer to play creepy-dungeon-organ music, followed by Lee unleashing a blood-curdling scream. It’s funny every time, and is quite an achievement, really — hitting those high “notes,” with that much power, on demand, is not that different than singing.

“I really can’t remember how that started,” says Lee, laughing. And as for the old show-biz shtick where Lee hits a quick, two-note bass riff to underscore a deadpan remark made by Letterman or a guest, Lee says he never knows in advance that the comment is coming, so he has to keep his ears open.

“There’s never any warm-up, and I have no access to the script,” says Lee. “The only one who does is Anton (Fig, the drummer). He has a list of the jokes from Dave’s opening monologue, so he can plan his rim shots in advance.”

Kevin Ransom is a free-lance writer who covers music for AnnArbor.com He can be reached at KevinRansom10@aol.com.