A trove of two dozen unfinished Bob Dylan songs written circa 1967 during his “Basement Tapes” period are being completed by an all-star band assembled by producer T Bone Burnett and including Elvis Costello, Marcus Mumford and My Morning Jacket’s Jim James for release as an album and Showtime special later this year.

“These are not B-level Dylan lyrics,” Burnett, 66, said Monday during a break in filming and recording sessions in Hollywood for the project titled “Lost On the River: The New Basement Tapes.” “They’re lyrics he just never got around to finishing.” Rounding out the band working on the new material are Carolina Chocolate Drops singer Rhiannon Giddens and Dawes lead guitarist and songwriter Taylor Goldsmith.

Burnett and Costello spoke of trying to honor the spirit of the original recordings that came to be known as “The Basement Tapes” because they were recorded by Dylan and the Band while they had holed up in a large house in upstate New York known as Big Pink.

The recordings they made were never intended to be released, but became the first widely circulated bootleg recordings by a major rock artist, and ultimately were released in official form by Dylan’s label, Columbia Records, in 1975.

Among the songs written during that time, many in collaboration with members of the Band, were some of the most highly regarded of both artists’ careers, including “I Shall Be Released,” “Quinn The Eskimo (The Mighty Quinn),” “Tears of Rage” “You Ain’t Goin’ Nowhere” and “Crash on the Levee (Down in the Flood).”

They reportedly wrote and recorded at least 30 new songs, but Dylan had written many more sets of lyrics that he never set to music.

“The New Basement Tapes” project aims to honor the freewheeling spirit of the original sessions, even though, Costello pointed out from the control room of Capitol Records Studio A, “This is the exact opposite of ‘The Basement Tapes’: We’re in the best recording studio in the world, and we’re not in a basement.’”

Another difference is that this project also is being documented by filmmaker Sam Jones, for Showtime’s Sho: Close Up documentary “Lost Songs: The Basement Tapes Continued.” Jones noted that no photographs apparently were taken during the original Big Pink sessions, although some film footage is said to exist.

One intriguing facet of the current project is the collaboration among the participants. Each has come up with his or her own music for many of the lyrics, resulting in multiple versions of the same songs and allowing a perspective on the ways different artists respond to Dylan’s lyrics.

Each artist acts as producer during the recording of his or her song, and all provide whatever instrumental support the others require.

During the first week of recording, Burnett said they’d laid down nearly 48 tracks and expect to have more than 50 to draw from by the time recording sessions wrap up this week. Among the songs are the title track, “Florida Key,” “Card Shark” and “Hi-De-Ho.”

“It runs the gamut from everybody having a blast in the studio to being really serious about doing things right,” Giddens said.

It hasn’t been decided how many of the tracks ultimately will be released. Dylan’s sole involvement in the project, beyond providing the lyrics, appears to be giving it his blessing.

A spokesman for Dylan said he’s offered no explanation of why he decided to offer the unfinished songs to Burnett to complete. It’s hard not to speculate that the decision is at least partially driven by his experience helping to bring lyrics left unfinished by Hank Williams at his death in 1953 to life by having a variety of rock, pop and country artists to set them to music and record them for the 2011 album “The Lost Notebooks of Hank Williams.”