St. Paul and the Broken Bones, a quickly rising neo-soul band from Birmingham, Alabama, has a famous fan in the soon-to-retire TV talk-show host David Letterman.

Earlier this month, astute music lover Letterman praised the band during an unprecedented two minute-plus introduction to the group’s “Late Show With David Letterman” debut.

“Are you guys ready?” he asked the group from his desk. “I’ll tell you a true story. The first time I heard this song (‘Call Me’), I was screaming till I cried. That’s what I want. Can you do that for me tonight?”

Bassist Jesse Phillips and his St. Paul and the Broken Bones bandmates, including frontman Paul Janeway, had expected a typically short intro. They were taken aback by their host’s heartfelt words.

“It was surreal,” Phillips said. “When he deviated from the cue cards, we started rustling around a little bit. We thought they would cut that out but they left it in.”

Reaction to the Letterman appearance has been strong, Phillips said.

“Everybody I see in the past couple of weeks has been like, ‘He loves you guys! I’ve never seen him be like with a band before!’ ”

In less than three years together, St. Paul and the Broken Bones has appeared with Letterman, played more than 300 shows and released an EP and a full-length album, “Half The City.”

Ben Tanner, keyboardist in the Alabama Shakes, produced the album in that legendary Alabama music city, Muscle Shoals. Tanner and his partner in the Florence-based Single Lock Records, John Paul White of the Civil Wars fame, signed the group to their record label.

Recording in Muscle Shoals, where Percy Sledge, Aretha Franklin, the Staple Singers and many more cut soul sides in the 1960s and ’70s, made musical and geographical sense for the Birmingham-based St. Paul and the Broken Bones.

“It’s not a tangible thing, but you do feel the vibe,” he added. “And there’s not a lot of image stuff there. It’s really about the music.”

Phillips felt some pressure during sessions at Nutthouse Studio and mixing at the famous FAME Studios.

“If you’re going to do it in Muscle Shoals, you want to make something cool,” he said. “You don’t want to be the one who doesn’t help carry the torch.”

The roots of St. Paul and the Broken Bones include the breakup of a Birmingham rock band that featured Janeway and Phillips. Later they met regularly at a local recording studio.

“After several months of that we needed some people to help us finish a few songs,” Phillips said. “We invited some of the other guys in, just to see how it felt.”

The Memphis soul, Stax and Hi records sound St. Paul and the Broken Bones developed derives in part from Janeway’s church-based vocal style.

“We wanted to frame his voice in the best way we could figure,” Phillips said. “We realized at some point that the best thing for it was that Stax, Muscle Shoals, little bit of rock ’n’ roll, blues, soulful thing. The last piece of the puzzle was bringing the B-3 Hammond organ in.”

Releasing Janeway from the guitar was another important move, Phillips said. “He used to play guitar a lot. That held him back. When we took that guitar out of his hands, he started dancing.”

Once the band started performing, reaction was immediate. Attendance grew every show.

“We were surprised,” Phillips said. “People were excited. We had the surprise factor on our side. People didn’t expect that much sound and energy from us. Paul opens his mouth and the horns start blasting. But we didn’t have a lot of expectations. We were just doing our thing.”