There’s an expression that Bill Hader lets play across his face at the end of the first episode of “Barry’s” new season. Pointing a gun at one of the show’s major characters, Barry orders them to comply with a plan he’s just coming up with on the fly; a grin flickers around his mouth, then takes root, as his eyes glimmer with self-belief far too serene to be disrupted by the knowledge that what he’s doing is madness.

HBO has requested that reviewers withhold key plot details of the next installment of “Barry,” TV’s darkest comedy or its funniest drama. So it’s impossible to explain more about the mechanics of that scene, or what Barry’s trying to do, beyond broad strokes. Suffice it to say that Barry, the assassin who has found in a nascent acting career a way to put his ability for self-deception to work, has landed upon a scheme that will allow him to feel as though his past sins are forgiven. That his way forward out of wrongdoing requires him to put those around him through a great deal of pain is an irony Barry cannot or will not consider.

Which makes for a richer and deeper character study than “Barry” has previously been, and feels like a pleasing reward for fans who’ve waited nearly three years for more of this story. In the past, this show (while always strong) sometimes seemed to require some audience patience as it set up its somewhat outlandish premise. That legwork is now done. Thanks to the show’s writing and to Hader’s remarkable performance, finding shades of meaning and expression within a character who presents at first as emotionally dead, we know exactly who Barry is. And we now get the complicated pleasure of watching him decompensate as he attempts to cheat his way toward an easy sort of redemption. In the scene described above, Barry’s more manically optimistic than we’ve ever seen him; in a later scene in which he’s demanding something of his girlfriend and fellow actor Sally (Sarah Goldberg), he’s as terrifying as we’ve ever seen him.

Part of the trick of “Barry’s” early going was that no one properly perceived just how bizarre and socially unacceptable Barry’s behavior was. To a group of actors, he just came off as “Method,” a sly joke on just how stretched that concept has become to accommodate all kinds of misbehavior. Now, though, the bill is coming due; Barry’s deciding that he needs to find a way out, even an easy one, coincides with the world losing its patience with him. Sally, a steady presence throughout this show’s run, has a powerful arc running parallel to Barry’s that ought to place Goldberg in the heart of the Emmys conversation. Because she’s enjoying the first flickers of real career success, she’s trying harder than ever not to see what’s right in front of her face, even as Barry’s alternating indifference and brutality just keep announcing themselves. That her career success comes from a personal work putting her own trauma on public view, even as Barry’s actively harming her in her present tense, lends Sally’s story an irony that’s drawn with a lovely sensibility, and no small amount of pain.

Goldberg will break your heart, but the details of her rise will startle you with just how cruelly funny and sharply observed they are. Show co-creators Hader and Alec Berg have, throughout the first two seasons, focused mainly on Hollywood’s bottom-feeders. Goldberg’s storyline shows that success doesn’t make Sally’s world any less venal or insecure (and selling one’s story may end up doing harm one can’t have anticipated). The writers make a point clearly: One can transcend one’s lowly, hollow circumstances, only to find that the circumstances have a way of following you up the ladder. The same’s true for Gene Cousineau (Henry Winkler), who is also attempting a fresh start. His attempts at mending fences with people he’s alienated run into the brick wall of his own personality, and the things he’s done that victims of his caprice can’t forget.

In an era of short-run, quick-catharsis limited series TV, “Barry” is now in the satisfying place of having accumulated real history and heft. Its story, about the impossibility of starting over, draws from our knowledge of just how much these characters have been through; in the hit-man half of the series, consequences seem to draw nearer and nearer for Barry, while Fuches (Stephen Root) and NoHo Hank (Anthony Carrigan) make their own attempts at reinvention. Once again, I’m limited by what HBO has indicated it believes to be a spoiler — suffice it to say that Barry is, in his delusional quest toward becoming a whole new man, in the dark about what his enemies’ plans to refresh themselves might mean for his personal safety.

“Barry,” then, is as juicily tense as it’s ever been. And it sets a new high for itself with a chase scene, deep into the season, that balances loopily unexpected humor with a real sense of peril. (It seems that last season’s episode “ronny/lily,” with its taekwondo-master tween girl nearly taking Barry out, set the precedent that there will be one jawdropping set piece per season, at least.) But the chaos and mania of Barry’s Hollywood life and his life of crime are, more than ever, serving what is a grand-scale character study. Barry’s fleetingly aware that something is, even by the standards of someone who seems to himself irreparably damaged, truly wrong. And his attempts to fix it through simply shouting the world around him into submission aren’t working, cannot work. The question the first six episodes of this fantastic season of television ask is put plainly, but might take the rest of the show to answer. What does one do when one wants forgiveness, but can’t just take it by force of will? It’s a conundrum even those of us lucky enough to be relatively undamaged can’t solve — little wonder that it’s pushed TV’s most fascinating protagonist to the brink.

“Barry’s” third season will premiere on HBO on Sunday, April 24, at 10 p.m. ET/PT.