Richard Thompson, left, and Loudon Wainwright III.

“Loud & Rich.”

That’s the wry, tongue-in-cheek “title” that Loudon Wainwright III and Richard Thompson chose for their co-headlining tour that comes to the Michigan Theater on Tuesday.

Knowing these guys, you might guess that one of them thought up the title first, as a joke — and then decided later to put together the tour. Or, you might think that it’s a parody of the commercial-country duo, Big & Rich. After all, Wainwright and Thompson are both known for their sharp wit — sometimes droll, sometimes sardonic — whether it’s in their songs, onstage or in conversation.

But both are also equally gifted when it comes to writing incisive songs that are packed with pathos and emotional candor — songs that can be prickly, harrowing or heartbreaking.

Which means, in short, that these two were made for each other, as far as being tour-mates. Indeed, they’ve toured together a few times in the past, they’ve known each other for more than 25 years, and Thompson produced two of Wainwright’s albums in the mid-to-late ‘80s. And, in fact, that’s actually where “Loud & Rich” comes from — that was the caption they dreamed up for a photo of the two of them on the back of Wainwright’s 1984 album, “I’m Alright.”

“It just seemed like a good idea for us to tour together again, and we’re having a great time,” says Wainwright by phone from a tour stop in Greensboro, North Carolina. “I’m a big fan of Richard’s work — his writing, and, obviously, his guitar playing, which is an amazing thing to watch and hear. I like his outlook, his songs — plus, he’s funny, he’s entertaining, and a he’s wonderful performer.”

The way the show is structured, Wainwright does a set, and is then joined by Thompson for a few songs. Then, Thompson does a set, and is later joined by Wainwright for a few more duets. “That’s a thrill, having Richard, with that kind of guitar virtuosity, backing you up when you’re singing your songs,” says Wainwright. “Now, when I join him, I’m not exactly going to add searing guitar solos, because I play rhythm guitar, but I sing with him.”

For the two collaborative sections, Wainwright and Thompson are drawing on a “pool of songs that includes some of mine, some of his, a Leiber and Stoller cover, and a couple of old Charlie Poole songs,” says Wainwright. (More on Poole later.)

Wainwright and Thompson have also each found themselves in an introspective/retrospective mood in the last couple of years. In 2008, Wainwright released a CD titled “Recovery,” for which he went into the studio with several backing musicians and re-recorded new, fleshed-out versions of his songs that he originally recorded, for the most part, as solo-acoustic tracks in the ‘70s.

Some of the new versions use darker or more sober textures, arrangements and vocal performances to provide a more mature, more thoughtful context to songs that, in many cases, Wainwright originally delivered in the wise-guy, ironic or sarcastic fashion he often favored as a young singer. For example (in the song “Motel Blues”), “when I originally sang the line, ‘Come up to my motel room, save my life,’ I was 25. But then, to record it again, at age 62, it adds a different perspective — an almost desperate kind of poignancy,” muses Wainwright, now 63.

"Motel Blues" - Loudon Wainwright III

More recently, in June, he released “High Wide & Handsome: The Charlie Poole Project,” a tribute to the country-music pioneer of the 1920s-‘30s.

Meanwhile, in August, Thompson released “Walking on a Wire,” a four-CD box set that spans his 40-year recording career, dating back to his 1968 beginnings with Fairport Convention. This was Thompson’s second box set in four years. In ’05, a British label released “RT: The Life & Music of Richard Thompson.” That ’05 box was more for fervent fans and completists, as it consisted mostly of previously unreleased alternate takes, rarities and relatively obscure live recordings

“Walking on a Wire” is aimed more at the non-obsessive Thompson fan who may or may not have heard all the fuss about Thompson’s songwriting brilliance and astonishing guitar chops, and wants an overview of Thompson’s music and career. All of the songs have previously been released, either on Fairport albums, his solo discs, or on the albums he made with his then-wife Linda Thompson between 1974 and 1982. In fact, the “Linda years” are especially well-represented, with 21 stellar tracks culled from those duo discs.

Listening to the entire box, over a period of a few days, one is once again dumbfounded that Thompson isn’t a household name, given that he’s one of the greatest and most innovative rock/folk guitarists of the last four decades. One aspect of his fretboard fireworks that makes him so unique is that, unlike most rock guitar heroes, his playing isn’t rooted in the blues. Instead, Thompson — a Brit with Scottish ancestry — draws on the sonic-drone quality of Celtic music when he lets fly with one of his speedy, death-defying solos. Talk about your “six-string razor.”

As for Wainwright’s Charlie Poole project: “I’ve been a big fan of Poole’s music for about 35 years, and he was a real unsung hero,” says Wainwright. “He wasn’t really a writer, but was a remarkable artist, banjo player and entertainer.

“There are parallels between him and some of the things I write about. He wrote novelty songs, and I’ve certainly written my share of silly songs, and we’ve both written drinking songs. Plus, like Poole, I was born in North Carolina — and then we moved up to suburban New York when I was about three years old. So, even though I didn’t grow up there, that whole southern sensibility has always had a real pull on me.”

Of the project’s 30 songs, 21 are Wainwright’s interpretations of tunes that were recorded or performed by Poole back in the ‘20s-‘30s. In addition, Wainwright and producer Dick Connette co-wrote nine new songs about “the life and times” of Poole. For inspiration, they traveled to Poole’s hometown of Spray, NC, and drew from “Ramblin’ Blues,” Kinney Rorrer's biography of Poole.

Over the last several years, Wainwright has also been devoting time to what is now a “second career” as an actor. He’s become friends with Judd Apatow, the über-writer/director/producer of raucous, profanely funny film comedies (and who is a big fan of Wainwright’s music) — and had small roles in Apatow’s two biggest hits: “The 40-Year-Old Virgin” and “Knocked Up.” More recently, Wainwright was in the children’s movie “G-Force,” and has appeared in a couple of episodes of “Parks and Recreation,” the Amy Poehler sitcom. “I really enjoy acting. It’s a different type of creative expression — it’s more collaborative than what I do with my music,” says Wainwright. “Plus, that SAG (Screen Actors Guild) health insurance is great.”

PREVIEW “Loud & Rich” Who: Co-headliners Loudon Wainwright III and Richard Thompson are both known as great writers of incisive songs that can be sardonically funny, heartbreaking, or emotionally harrowing. What: Wainwright falls into the contemporary-folk category, while Thompson is a British-folk-rock pioneer and guitar hero. The show consists of a separate set by each, plus two short sets where they join forces. Where: Michigan Theater, 603 E. Liberty St. When: Tuesday, 7:30 p.m. How much: $65, $39.50, $25. Details: 734-668-8397, 734-763-TKTS, Michigan Theater web site.