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One of the tectonic shifts in crime TV has been linking the detective’s personal life to the crime at hand. You can create twice as much drama if you’ve got both a grisly murder and an unsettled cop — preferably the intriguing likes of Helen Mirren in “Prime Suspect” or Idris Elba in early “Luther” — acting out all over the case.

But that link needs to be believable to work, something “Law & Order: SVU” hasn’t nearly mastered. One of the best series to convincingly bind together a cop and her case was “Top of the Lake,” the riveting 2013 series from Jane Campion and Gerard Lee. Elisabeth Moss’s Robin Griffin is a Sydney detective who visits her New Zealand home, where the disappearance of a 12-year-old draws her in close proximity — literally and psychologically — to the men who raped her as a teen. As with the equally powerful and grim “Happy Valley,” the links fit together naturally, without requiring the broad, convenient coincidences frowned upon in detective lit circles. Robin faced her demons, and in the process, the murder story explored the deep roots of misogyny and the culture of rape.

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Alas, the show returns to SundanceTV on Sunday at 9 as a lesser thing — engaging and entertaining, for sure, but lazily written (all six episodes will be shown over three nights). All the forced coincidences will make your eyes roll, as if Australia is some kind of tiny town where everyone just happens to be connected somehow, criminally and/or romantically. And the themes of patriarchy and female friendship that grounded the first season do return in “China Girl,” along with added ideas about motherhood, but it all plays out with less subtlety and less emotional weight. The central villain this time, a pompous louse named Puss (David Dencik), is one-dimensional enough to be boring — never a good thing. He’s an abusive man in power, and I suspect that’s all we’re supposed to think about him.

Puss objectifies women, and so do a klatch of young geeks who meet in a coffee shop and talk about the hookers they follow online. They can’t deal with the real thing, although one of them has a GFE (“Girlfriend Experience”) relationship with one of the women in Puss’s house — that’s their connection to the case. The problem isn’t necessarily that most of the men in “China Girl” are dislikable and, to one degree or another, sexist; it’s that they’re not particularly well-drawn or believable.

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It’s a shame the story doesn’t fully work, because some of the acting in “Top of the Lake: China Girl” is top of the line. I love the cast, even when the script fails them and they’re forced to make illogical scenes work. This time, Robin is getting back to work in Sydney when a body washes up on the beach inside a suitcase. The body, we know right away, is somehow connected to Puss’s brothel. Robin takes the case, and she is forced to mentor a less experienced cop, Miranda (Gwendoline Christie). Meanwhile, still healing from the Kiwi case, she seeks out the daughter she gave birth to after the rape 17 years ago. Raised by well-to-do couple Julia (Nicole Kidman) and Pyke (Ewen Leslie) Edwards, Mary (Alice Englert) has been misbehaving since she learned her parents are breaking up and Julia is in love with a woman.

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Moss continues to prove, as she has in “Mad Men” and “The Handmaid’s Tale,” that she’s among the best actors working in TV right now. As Robin, she is weary, driven to avoid old wounds by throwing herself into the suitcase mystery. But she can’t help herself from looking into Mary, after the events of season one. In Robin’s scenes with Mary, you can see countless emotions playing out clearly but quietly on Moss’s face — the pain and guilt of not raising her daughter, the gratitude that her daughter likes her, the strangeness of having a daughter who is almost an adult. Englert is a good scene partner for Moss, but her role is stunted in other parts of the series, since she’s in love with someone with whom she has absolutely no chemistry.

Kidman is also very good, even though Julia is so irritating in her feminist cant — or rather, because Julia is so successfully irritating. She’s a devoted mother to Mary, but she’s also dealing with her own life changes, frustrated that her newfound freedom is tethered to Mary’s newfound rebellion. I wish Kidman were more prominent in the series, rather than a supporting character, but she brings authenticity to every scene she’s in. Christie, best know for her work as Brienne on “Game of Thrones,” is likable here, as she and Robin work through the incompatibilities of their partnership. Miranda is an offbeat sort, which Christie pulls off beautifully.

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“Top of the Lake” is a distinctive and compelling franchise, despite the weaknesses of “China Girl.” Next time, and I do want a next time, let’s hope the writing is up to the acting.

TOP OF THE LAKE: CHINA GIRL

Starring: Elisabeth Moss, Nicole Kidman, Alice Englert, Gwendoline Christie, David Dencik, Clayton Jacobson, Ewen Leslie. On SundanceTV, Sunday, Monday, and Tuesday nights, 9-11 p.m.


Matthew Gilbert can be reached at gilbert@globe.com. Follow him on Twitter @MatthewGilbert.