NEW YORK — Louis Daniel Armstrong, variously nicknamed “Satchmo” and “Pops,” is the subject of “A Wonderful World,” a musically rich if wordy and information-heavy Broadway show that serves as a reminder of just how challenging the jukebox biographical genre can be, even when you have a star of the level of craft and talent evidenced by James Monroe Iglehart.

That ebullient actor, best known for playing the Genie in Disney’s Broadway “Aladdin” and clearly determined to challenge himself in his career, does an admirably courageous dive here into Louis Armstrong, trying to capture not just his famous exterior smile, unifying persona and performative panache but also the reasons for his famously intense level of infidelity that led to a trail of dismayed former wives, each loved and then discarded by a man wrestling with lifelong demons.

“Wonderful World,” which I first saw in its pre-Broadway Chicago tryout, tries inestimably hard to deliver the music associated with Armstrong to a Broadway audience (with a hefty share of international tourists) likely to have bought a ticket to hear big band sounds and New Orleans-style jazz while simultaneously honoring Armstrong’s massive role in popularizing the role of brass in jazz.

“You can’t play anything on a horn that Louis hasn’t played,” Miles Davis famously once said.

At the same time, though, the show also wants to explore the complexity of Armstrong’s relationship with the Black community, contemporaneous and otherwise, who often saw him as a smiling sell-out, lugubriously vamping lyricist Jerry Herman through his wide, toothy grin and becoming a figure easily used by politicians like Richard Nixon as a way of papering over inequity and overt racism.

The reshuffled creative team has done a lot of stellar work, especially with the book, now credited to Aurin Squire, with Andrew Delaplaine and the show’s director Christopher Renshaw listed as “co-conceivors.” This new version puts Armstrong as the narrator of his own story, rather than his wives as previously was the case. Those women, performed by a powerful and vulnerable quartet of Dionne Figgins (as Daisy Parker), Kim Exum (Alpha Smith), Darlesia Cearcy (Lucille Wilson) and Jennie Harney-Fleming (Lil Hardin) now get to be themselves and sing vivaciously, rather than constantly having to talk about their unfaithful husband.

But “Wonderful World” still has to deal with a very complex central persona who does not easily fit inside the classic jukebox narrative of fast rise from nowhere, stardom granted, bad mistakes made on the road, belated personal understanding achieved and broad redemption found.

Thanks to the era and circumstances of his rise, Armstrong had much that remained unresolved inside his head and a lingering bitterness, all of which this show, and especially its lead, tries to honestly capture. It’s hard, though, and, at times, it feels like Iglehart gets weighed down by the sheer heft of the responsibility he feels not to sugarcoat his man.

If he let go more, his performance would have more pop and attention. Still, I very much admire his approach.

The show also has to deal with a central figure known for panache on the solo trumpet as much as his vocals, which presents its own challenges, although that issue, too, is greatly improved from the tryout. It is easy now to accept that the trumpet is coming (mostly) from the orchestra, although I think that made the show hesitant to really focus on Armstrong’s skills with the instrument. Understandably so.

To showcase and to dissect always are tricky, twin ambitions for any jukebox show, and I think the main problem with “Wonderful World” is that it worries too much about the latter, which gets in the way of fully delivering the former. The show, which organizes itself around Armstrong’s career-defining travels from New Orleans to Chicago to Hollywood to New York, has a whole lot of biographical information to deliver and it’s a very heavy load, especially in Act 2, which becomes a bit of a slog when audiences at such shows long have been conditioned mostly to expect a concert-style finale. In the Wikipedia age, information is not what audiences want so much as a point of view and, well, lots of songs and music. We still could do with less history and more time with Louis and his band.

All that said, there is much American music here to enjoy (orchestrations and arrangements are credited to Branford Marsalis), including styles rarely heard these days on Broadway or anywhere else live, from “It’s Tight Like That” to “Kiss of Fire” to “Up a Lazy River,” as well as Armstrong’s softer biggest hits like “Hello Dolly” and the title number. The choreography from Rickey Tripp is gutsy and, among a very capable company, there’s a highly skilled cameo from DeWitt Fleming Jr., who had the courage and skill to jump inside Lincoln Perry (otherwise known as Stepin Fetchit).

But you always feel like the show is racing against time. Maybe that’s actually a pretty fair accounting of Armstrong’s life.

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At Studio 54, 254 W. 54th St, New York; louisarmstrongmusical.com.

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