If you’re inclined to like Jack White, Tuesday night’s show was a complete presentation — from the merchandise table, which had a longer line than the bars in the Saenger Theatre, to his Third Man Records logo integrated into the blue and white lighting grid above the stage.

If you’re not, the show gave you reason to think White has control issues. Both points of view are probably true, but you’d have to dislike classic rock ’n’ roll values to argue with the show.

From the start and “High Ball Stepper” from his upcoming album, “Lazaretto,” White presented a sonically detailed, thought-through rock sound that filtered the blues through glam, metal and punk, often to Led Zeppelin-like effect.

Unlike at most concerts, the kick drum, snare and bass were dialed back to a civilized relationship with the other instruments in the band, allowing two keyboards, the violin and vocal harmonies of Lillie Mae Rische and a pedal steel guitar to be heard even though White’s guitar raged as the centerpiece it is in his music.

As he did during his set at the Voodoo Music Experience in 2012, White played music from all phases of his career, with a heavy dose of the White Stripes, along with music from the Raconteurs and songs from his solo albums, “Blunderbuss” and “Lazaretto.” Only the Dead Weather songs were omitted entirely.

When he last played New Orleans, he also covered New Orleans piano legend’s James Booker’s “Papa Was a Rascal.” This time, he sent everybody into the night with a sing-along version of another Louisiana classic, Leadbelly’s “Goodnight Irene.”

“We can’t be in Louisiana and not play this one,” he said to introduce it.

White didn’t forget Booker this time, either. He didn’t play his songs, but when he performed the new song “Three Women” on an upright piano, he finished with a celebratory “Take that, James Booker.”

Throughout the hour-and-a-half show, White nodded again and again to American roots music, whether it was by referencing its greats or borrowing from country, as he did most obviously on the new “Temporary Ground,” a duet he sang with Rische.

No matter the genre, though, White made it all into rock ’n’ roll. Little in the night grooved, even on the rare occasion when drummer Daru Jones tried to insert some swing. Instead, White songs stomp, and Jones was able to fuel that just fine, often pounding a floor tom and crash cymbal in an exhilarating caveman beat.

It’s a tribute to the immediacy of White’s songwriting that he was able to play six songs from the upcoming “Lazaretto” without any weakening of audience engagement.

The slowest moment came during “Alone in My Home,” but it was also the song that sent up emotional red flags as he sang with Rische about how he’s “lost feelings of love,” he’s “becoming a ghost so no one can know me,” and “alone in my home/no one can touch me.”

His tumultuous personal life these days includes an ugly divorce and bits of bad behavior that sometimes leave him apologizing, most recently to the Black Keys’ Dan Auerbach; it was hard not to hear “Alone in My Home” as an expression of that upheaval.

Nothing else White played Tuesday night felt that naked, and he quickly changed the mood with a punk-rock version of a new song, “Just One Drink,” and a ridiculously heavy “Seven Nation Army,” playing the latter on a guitar that was distorted to such a degree that its tuning was irrelevant.

It was exactly the sort of rock ’n’ roll moment people came for, and White delivered on a regular basis.

The concert didn’t allow the audience to feel any closer to White, but the man Rolling Stone has dubbed “rock ’n’ roll’s Willy Wonka” isn’t in the business of letting us see more than he wants.

Alex Rawls writes about music. Contact him at my spiltmilk.com.