One of the least famous but most revealing radical arguments of Hannah Gadsby’s breakthrough special, “Nanette,” is that we should only dress babies in the color blue. Sorry pink. Pointing out how blue is associated with coolness as well as the hottest part of the flame, she said with admiration that it’s full of contradictions. So is her comedy.

Gadsby earned rapturous reviews and a ferocious backlash pushing the boundaries of stand-up by insisting on its limits in that show. The cultural phenomenon of “Nanette” haunts her follow-up, “Douglas,” now on Netflix, and in typical self-awareness, she acknowledges that specter at the start. In a daring formal move, she says she will manage expectations by providing a road map for the show. There will be some needling of the patriarchy, a little observational comedy, some stuff about her autism, a lecture for her haters and a Louis C.K. joke she promises will be great. (It’s fine.) This is an old magician’s trick, telling the crowd what you are going to do, only to still startle them with it.

“Douglas” is a surprisingly slick, joke-dense show, running hot then cold and even chilly, periodically pausing to meditate on its changing temperature. Wearing a blue suit, Gadsby begins by pointing to a prop dog made of crayons onstage, immediately making fun of herself, a notable shift since “Nanette,” when she inveighed against self-deprecation. As she has said in interviews, she is now a “high status comedian,” and her production reflects that, with strategic lighting, visual jokes and an obsessive focus on the response to her own success.

This new work seems less ambitious but isn’t. If anything, it’s formally more complex and denser intellectually, if far less confessional. Whereas “Nanette” needed to stop the comedy to make its most serious points, Gadsby works hard to blend the two here, and the result is an intricate, heady show whose cleverness gets in its own way. She refers to it, aptly, as her “difficult second album.”

Doubling down on the comedy of contradiction, Gadsby tells you the show has not started during the actual show. “Confidence makes you stupid,” she says in a bit about Americans. “I’m very confident in that.”

That is the kind of delightful quip you might say out of the corner of your mouth while shaking a cigar. But like her meta-commentary, it keeps you at a distance. When she performed this show in New York last year, Gadsby, in a discussion of her autism, built to a story about a girlfriend who insulted her with a slur. This made the audience gasp but also threw the show off balance. She cut it for Netflix. It was a smart edit — that story felt like a strained and doomed attempt to capture the gut-punch emotional climax of “Nanette” — and the omission suits the prickly puppet-master vibe of this new effort.

Often tagging her jokes with a statement of purpose, she says quite explicitly: “I’m not here to collect your pity. I’m here to disrupt your confidence.”

In a raging bit about the anti-vaccination movement, Gadsby pokes fun at her fan base, calling her core demographic “rich white entitled women,” and when she finishes a point about the corrosiveness of the phrase “boys will be boys,” she hushes the clapping. “This is not a rally,” she says, flashing a smile.

Gadsby saves most of her scorn for her critics, particularly those whose response to the novelty of her work was to write her out of comedy. Not only does she list all the ways people derisively classified her work — as a lecture, a one-woman show, a TED Talk — she also spoofs each mode.

Gadsby often seems so annoyed by the (dumb) idea that she wasn’t trying to be funny that she overcompensates, proving she can do conventional stand-up jokes, too. She goes after big targets — Taylor Swift, Harry Potter, fad diets, golf — and leans on some familiar joke conventions (the women in the crowd are thinking this, the men are thinking that). There are riffs on language that you could have found on BuzzFeed years ago (Why do Americans call petrol gas when it’s a liquid?).

She warns us early on that her observational comedy isn’t that good, but self-awareness does not turn a mediocre joke into something better. Gadsby is an artist who thinks like a critic, but her critical side sometimes functions as a protective mechanism, a safety net she doesn’t need.

Gadsby is at her best and most distinctive when she is talking about art, and she uses the history of paintings the way “The Daily Show” employs clips of politicians spouting rhetoric. Her jokes here balance smart and silly, skewering, for instance, the vast number of artworks in museums showcasing naked women on rocks. She does another funny bit about the Teenage Mutant Ninja Turtles (which she also mentioned in “Nanette”), zeroing in on their art-world names. For Gadsby, names and naming matter. It’s perhaps the ultimate power.

This may be why she seems so fixated with how others label her work.

Early on, she describes her show, dryly, as a romantic comedy. She categorizes constantly and in so doing, makes categories seem ridiculous. Another contradiction. But on this subject, how to define her work, she does not leave it there. After she does a comic bit about prepositions, Gadsby lays her cards on the table. “What this show is,” she says dramatically and at a speed that is tough to follow, “is a metaphorical preposition that explains the relationship between what you think you think you see me think and what I’m genuinely able to think.”

It’s a mouthful and invites analysis. One thing it suggests is that Gadsby remains skeptical about the ability of comedy to express oneself honestly. There’s enough of a difference between what she says onstage and how it’s perceived that her show is about that incongruity. But what’s also important about her language here is that she emphasizes the act of thinking as much as its conclusions.

As renowned as she is for righteous political comedy, Hannah Gadsby is an aesthete alert to form, a comic whose means of mocking sexist systems of power is to home in on the meaning of the color blue. Contradictions are a problem for a debater, but not necessarily an artist, or certainly a comedian. They are often where the fun is. And so when she says, “There is beauty in the way I think,” you have to agree but also wonder: Is this confidence or the opposite?

© 2020 The New York Times Company