Jolly Fingers: Chestnut is happily stuck on Elvis.

For a mainstream, hard-bop jazz pianist, especially a traditionalist like Cyrus Chestnut, an album of songs made famous by Elvis Presley makes no apparent sense. Elvis’ myth is so powerful that most of his hits are synonymous with him. More to the point, so many of those hits were simplistic, cliché-ridden fluff salvaged only by the King’s formidable talent.

But on Cyrus Plays Elvis, Chestnut finds a kindred spirit in Presley, a fellow gospel and blues devotee who once boasted that he knew “practically every religious song ever written.” It’s a surprise that the pianist could find the singer’s biggest hits so malleable and bountiful, but the connection between the two is obvious, and after one listen, this outwardly unusual trio project (with bassist Dezron Douglas and drummer Neal Smith) seems to have always been inevitable. Rarely does Chestnut tread in Presley’s footsteps, though in reinventing almost every track, he proves that he understands the King’s MO.

Take Presley’s 1956 hit “Hound Dog,” which originated with Big Mama Thornton’s nasty roadhouse blues four years earlier; Presley retained Thornton’s rawness, swagger, and blues, but he traded her contempt for grin-and-a-wink mockery. Chestnut, in turn, keeps Presley’s good nature, but he polishes “Hound Dog” and actually downplays the blues. If anything, his version is a joyful spiritual: Concentrate and you can practically hear a jubilee choir shouting, “They said you was high class/That was just a lie.” You can even do the holy dance to the clever, rollicking rhythms in Chestnut’s solo. The Elvis who was so willing to overhaul “Hound Dog” in the first place would surely approve.

Such sly transformations run rampant on Cyrus Plays Elvis. “Love Me Tender” becomes a dreamy Tin Pan Alley waltz, and a sprightly, swinging samba bounces out of “It’s Now or Never.” Spectacularly, the emblematic “Heartbreak Hotel” explodes into a concerto for piano, drums, and despair. Smith plays the snare and bass drums like gongs and crashes the cymbals for all they’re worth as Chestnut creates roaring, roiling chords and tremolos that sound like the ocean at high tide. Douglas is in there too, anchoring the other two as though they might run away without him.

Chestnut only fails when he lets trite melodies speak for themselves. “Can’t Help Falling in Love,” done smooth-jazz style with a Fender Rhodes and Mark Gross’ soprano sax, is a cheesy debacle, less for its arrangement than its earnestness: It sounds like the work of a bad wedding band. (Another ballad, “Don’t,” is acoustic and little better.) As though aware of the missteps, Chestnut counters with his original “Graceland,” whose hard-swinging melody stands on its own—and would be more fun at a reception.

Cyrus Plays Elvis isn’t a tribute album so much as an attempt to see if a cluster of the King’s songs work when his persona is stripped away. The material is still mediocre; it’s just that Chestnut’s musical personality makes magic with it. In an autumnal, thoughtful rendition of “In the Ghetto,” he even manages to simultaneously recast and reinforce Elvis’ interpretation. In contrast to the original’s weepy strings and backup voices, Chestnut works in minimalist textures, paring down even bass and drum accompaniment; that subtlety, though, matches the unadorned quiet of Elvis’ 1969 vocal. Neither “In the Ghetto” nor any other cut here is likely to eclipse the originals in the world’s esteem, but they introduce the possibility that someday, something might.