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Let’s face it: HBO doesn’t expect many people to watch the final mini-season of “Treme,” which explains its sentencing to scheduling Siberia — five consecutive Sundays in December. Yet co-creator David Simon (“The Wire”) has earned the right to finish his story, even if it’s one of limited dramatic heft. In a way, what Simon has said about the show is telling: Despite its efforts to dramatize the plight of New Orleans post-Hurricane Katrina, the more enduring legacy might be simply pumping money into the city via the show’s lavish showcasing of the area’s music and cuisine.

From that perspective, “Treme” might be classified as much as a heartfelt public-service announcement as a fully satisfying drama. And while the show boasted a gaudy array of talent, its commentary on the Crescent City and national indifference to its struggles seemed to dissipate as the seasons progressed, moving farther away from the fresh wound of the disaster.

It’s easy, of course, to admire Simon (who co-created the show with Eric Overmyer) for sticking to his artistic guns, which included adopting a slice-of-life approach that largely eschewed big dramatic flourishes. A season-one suicide that, oddly, felt almost like a fitting climax, and the rape of a key character in season three, played wrenchingly by Khandi Alexander, would be rare exceptions.

In keeping with its tone throughout, this last flight of “Treme” doesn’t exactly race around tying up loose ends, although it does provide elements of closure, or at least advancement, for most key participants. While the premiere opens with the enthusiasm surrounding the election of Barack Obama in 2008, it’s clear what ails New Orleans won’t be cured by a few buoyant chants of “Yes We Can.”

By now it’s 38 months after Katrina, and the web of relationships has shifted, sometimes in unexpected ways. Albert (Clarke Peters) is dealing with his cancer. Antoine (Wendell Pierce) is still trying to mentor kids as a music teacher, while Terry (David Morse) continues to push back against the police bureaucracy. And so on.

Yet even with the occasional ray of hope, Simon’s general outlook is too bleak to provide much consolation, either for his characters or for the show’s small but loyal audience.

Having watched all of “Treme,” it’s possible to admire the vision — and the performances by Alexander, Pierce, Peters, Morse, Kim Dickens, and Lucia Micarelli, among others — without feeling like the enterprise was a success.

Admittedly, part of that has to do, personally speaking, with modest appreciation of New Orleans jazz — or for that matter, the intricacies of creole cooking — that left the extended and abundant performance sequences feeling frequently like they brought the story to a halt. Ditto for stiff cameos by renowned musicians and chefs, generally demonstrating that not everyone is cut out to act.

Simon set the creative bar extraordinarily high for himself with “The Wire” and “Generation Kill,” and HBO has provided him and his collaborators the latitude to continue to do so.

Occasionally beautiful and emotional, but also bleak and frustrating, “Treme” certainly hasn’t sullied that reputation. Yet despite the writer’s contention that it’s his best show, for all but those few who savored every note, this rumination on a beleaguered The Big Easy doesn’t belong in the august company of those earlier gems.

TV Review: ‘Treme’

<p>(Series; HBO, Sun. Dec. 1, 9 p.m.)</p>

  • Production: <p>Filmed in New Orleans by Blown Deadline Prods.</p>
  • Crew: <p>Executive producers, David Simon, Eric Overmyer, Nina Kostroff Noble, George Pelecanos, Carolyn Strauss; producer, Joseph Incaprera; director, Anthony Hemingway; writer, Simon; story by Simon, Overmyer, Pelecanos. 60 MIN.</p>
  • Cast: <p>Wendell Pierce, Khandi Alexander, Clarke Peters, Rob Brown, Steve Zahn, Kim Dickens, Melissa Leo, Lucia Micarelli, Michiel Huisman, David Morse, Jon Seda, Nelson Hidalgo, India Ennenga, Chris Coy.</p>
  • Music By: