If the socks and sandals depicted on the back of the CD booklet don’t give it away, the solo piano opening, “Delores’ Boyfriend,” does: “American Tunes” is an Allen Toussaint album.

With its playful pauses and sly winks, “Delores’ Boyfriend” is unmistakably AT, colored with a distinctly Big Easy tinge, but neither bound nor overwhelmed by it.

“American Tunes” is a sort of posthumous sequel to “The Bright Mississippi,” the sparkling 2009 release that reasserted Toussaint’s jazz bonafides. Like that album, “American Tunes” was produced by Joe Henry, who has guided several veteran artists through the process of rediscovering themselves. He also produced Toussaint’s 2006 collaboration with Elvis Costello, “The River in Reverse,” the album that launched Toussaint’s post-Katrina rebirth as a touring artist.

Just as the Black Keys’ Dan Auerbach did when producing Dr. John’s brilliant 2012 comeback “Locked Down,” Henry took Toussaint out of his comfort zone and surrounded him with non-New Orleanian musicians. The idea was to free up the artist to follow stylistic threads wherever they lead.

David Piltch’s upright bass and Jay Bellerose’s minimal drums on Fats Waller’s “Viper’s Drag,” the second track on “American Tunes,” are testament to the backing band’s restraint and good taste, qualities Toussaint admired. Guitarists Bill Frisell and Greg Leisz are similarly inclined. They all set down “Confession’ (That I Love You)” for a soft landing.

New Orleans piano legend Henry Roeland Byrd, aka Professor Longhair, was a major influence on Toussaint. Toussaint reimagines Longhair’s “Mardi Gras in New Orleans” like Vince Guaraldi — the jazz pianist who scored the Charlie Brown animated TV specials — might have. Longhair’s original arrangement marched inexorably to the party. Toussaint, in his ultimately somber solo piano rendition, takes his time to meander and explore side roads. It’s a revelation. He’s more faithful to Longhair’s “Hey Little Girl.”

Another Mardi Gras standard, Earl King’s “Big Chief,” is deceptively familiar in its early going; the solo piano intro is instantly recognizable. But Toussaint then takes a dramatic detour, before returning to the melody at the end.

A listener will be tempted to lean in to the quiet opening of Earl “Fatha” Hines’ “Rosetta.” Again, Bellerose and Piltch are understated and simpatico. A lovely take on Billy Strayhorn’s “Lotus Blossom” finds Toussaint’s elegant piano paired with Charles Lloyd’s equally evocative saxophone.

A modest Latin rhythm percolates beneath the surface of Bill Evans’ “Waltz For Debby,” which, as New Orleans author and jazz scholar Tom Piazza points out in his liner notes, veers out of waltz time.

Eight songs in, Rhiannon Giddens, a cofounder of the traditional string ensemble the Carolina Chocolate Drops who also studied opera at Oberlin Conservatory, steps in with the album’s first vocals, for Duke Ellington’s “Rocks in My Bed.” Mahalia Jackson’s approach to another Ellington song, “Come Sunday,” was obviously a reference point for Giddens’ take on “American Tunes.” Toussaint spent the majority of his career writing for, producing and accompanying singers. The Giddens tracks are representative of that element of his history, even if they are a bit out of step with the instrumental arrangements that otherwise dominate “American Tunes.”

If grandiosity can somehow be subtle, it is on Louis Moreau Gottschalk’s “Danza, Op. 33.” Van Dyke Parks contributed the modest orchestral arrangement of cello and harp, as well as a second piano alongside Toussaint’s.

“Southern Nights” is among AT’s best-known compositions. Here, he and Parks team up for a two-piano take that finds the middle ground between Glen Campbell’s country-pop hit and Toussaint’s far moodier, original conception.

The album’s solo piano pieces were recorded in May 2013 in New Orleans. Tracks with the band were cut in Hollywood in early October 2015 — barely one month before a heart attack felled the 77-year-old Toussaint following a concert in Madrid.

He did not know that “American Tunes” would be his final fully conceived and completed album. But it stands as an elegantly tailored statement of where his late-career renaissance, informed by all that came before it, led him.

It closes with “American Tune,” the Paul Simon composition from which the album derives its title. It is also the only song on the album that Toussaint sings himself, and is reportedly the last song he ever recorded. Accompanied primarily by Adam Levy’s gut-string guitar, he quietly navigates such lines as, “I’m just weary to my bones/Still, you don’t expect to be bright and bon vivant/So far away from home.”

The final words we hear from him? “And I’m trying to get some rest/That’s all I’m trying to get, some rest.”

He more than earned it.

Follow Keith Spera on Twitter, @KeithSpera.