Every show on Tori Amos’ current "Native Invader" tour has been different. Her New Orleans performance was a whole other degree of different.

She changes her set list nightly, but has consistently opened with “iieee,” a track from her 1998 album “From the Choirgirl Hotel.” At a full Mahalia Jackson Theater on Tuesday, she introduced herself with an especially sensual, bewitching “House of the Rising Sun,” the traditional folk song the Animals turned into a hit. Alone onstage, alternating between electric keyboards and a grand piano, Amos sang, low and slow, that New Orleans has “been the ruin of many a poor girl.”

To the contrary, New Orleans seemed to inspire her.

Normally, she limits cover songs to two during a segment of the show dubbed the “Fake Muse Network.” Her 16-song, hour-and-10-minute New Orleans set encompassed seven covers, nearly as many as her own compositions.

But Amos’ art is as much about the drama of her voice and arrangements as it is about her writing. In New Orleans, she was a Siren Sinatra, skillfully interpreting other composers’ works and making them her own.

Some fans may have been disappointed not to hear more of her own material, or such signature early hits as “Caught in a Lite Sneeze,” “Cornflake Girl,” “Silent All These Years” and “Crucify.” Instead, she dug out “Leather,” a baroque pop singalong from her 1992 debut “Little Earthquakes.” And “Tombigbee,” an obscurity she apparently hadn’t performed in years. She completely ignored her latest album, "Native Invader."

She opted instead to acknowledge where she was. When fellow piano player Billy Joel performed at the Smoothie King Center in February, he saluted New Orleans with a plethora of songs that mention the city by name. Amos paid similar tribute. She followed “House of the Rising Sun” with the tour debut of her decade-old “Bouncing Off Clouds,” altering the “make it easy” line to reference the Big Easy. Next up? “Me and Bobby McGee,” with its name-check of both Baton Rouge and New Orleans.

She didn’t speak much between songs, instead shuffling sheet music and plunging into the next number. But she did give a shout-out to Steve Himelfarb, proprietor of local bakery the Cake Cafe. Himelfarb and Amos grew up as neighbors and friends in Maryland; both harbored music industry aspirations. After Himelfarb moved to Los Angeles and got a job at Capitol Records, he lobbied Amos to join him in California, which she eventually did. He subsequently helped her assemble her first band. “I wouldn’t be here without this person,” Amos said from the stage. “So thanks, Steve.”

(Also in attendance Tuesday: Carlo Nuccio, the local drummer who performed on Amos’ first two albums.)

A preacher’s daughter, she revived the hymn “Amazing Grace,” gorgeously, on the grand piano. She caressed the Cure’s “Lovesong” into something as sumptuous as it is sad. Steely Dan’s “Do It Again” didn’t offer as much space for her to color in.

But George Gershwin’s “Summertime” was a revelation. She pressed hard on the piano’s keys as she savored elongated syllables between breathy pauses and catches. With U2’s “Running To Stand Still," she built an intricate architecture of just voice and piano, marked by her distinct cadence, timing and tempo. For the final line, she teased out “running to stand….,” then repeated “still” eight times.

The encore opened with “Leather.” After a bit of “Programmable Soda” – another first for the current tour – she continued with “Precious Things,” a frank, unflinching calling-out of hypocrites.

The pounding, pre-recorded percussion and swirling lights of the concluding "Raspberry Swirl" were jarring, given the tone of all that had come before. She’s deployed “Raspberry Swirl” as the finale at several stops on her current tour. The most conventional moment of her artful night in New Orleans was also its least effective.

Follow Keith Spera on Twitter, @KeithSpera.

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Keith Spera writes about music, culture and his kids.