Fool me once, shame on you. Fool me twice, shame on me. But are viewers about to be fooled a third time by AMC's "The Killing"?

Two years ago, "The Killing" premiered with so much promise. It would take the familiar, stale format of the TV police procedural and give it greater depth and power and artistry by devoting an entire season to the investigation of a single murder case. Though the creative team (mainly writer/producer Veena Sud) and AMC publicity were very careful to never say that the murder of Seattle teen Rosie Larsen would be solved during that first season, it was so strongly implied that there was great viewer and critical outrage when it ended instead on a cliffhanger. The problem wasn't even so much that the show had failed to identify the killer, but that it had failed at so many of the other things it promised: the characters were mostly two-dimensional sketches, the plotting leaned too much on red herrings and enormous coincidences, the political side story never felt like a part of the rest of the show, and the atmosphere was largely generated by a comically overworked rain machine. By the time most viewers got to the end of that first season, they wanted to know whodunnit because it was the only thing the show had left to offer them, other than the chance to watch fine performances by actors like Joel Kinnaman (ex-junkie detective Stephen Holder) and Michelle Forbes and Brent Sexton (Rosie's grieving parents).

Season 2 made some marginal improvements — at the very least making some of the supporting characters feel like people — but was saddled with too much of what had been set up the year before. The mayoral election couldn't be dropped — and was resolved amusingly by a "viral" video whose 1200 views somehow swung things for Billy Campbell's underdog candidate — and Sud made other strange miscalculations like sending Forbes' character out of town for much of the season. And the mystery's solution was an astonishing Rube Goldberg contraption: that Rosie just happened to be in the wrong hotel room at the wrong time to eavesdrop on talk of an illegal political conspiracy, that Rosie's Aunt Terry just happened to be having an affair with one of the married conspirators, that Rosie was thrown into a car trunk and driven into a lake where Aunt Terry was waiting with her lover, and Terry (trying to keep her boyfriend from going back to his wife) pushed it into the lake, knowing there was a girl in the trunk but not that it was her niece. Like everything other plot twist on "The Killing," it was all one horrible, ironic coincidence.

Ratings slipped, critics did not look on the show any more kindly, and AMC execs cut their losses and canceled the show. But then faced with a potential programming shortage, they resurrected it with Sud still in charge, but with at least one lesson learned: in announcing the third season (which has a two-hour premiere Sunday night at 8, before regularly airing at 9 before "Mad Men"), AMC said unequivocally that "Season 3 will focus on a new case, which will be resolved over the course of 12 episodes."

The two-hour premiere suggests Sud and company learned at least a few other things over the course of those problematic early seasons.

The new season picks up a little over a year after the last one concluded with the election, the arrest of Aunt Terry, and Mireille Enos' over-invested cop Sarah Linden walking away from Holder and the job. Holder is climbing the ladder at the Seattle PD with the advice of new partner Carl Reddick (Gregg Henry) when he catches the murder of a teenage prostitute who was killed in a manner very similar to a case that Linden worked years before with her old partner James Skinner (Elias Koteas). Linden and Skinner arrested their victim's husband, Ray Seward (Peter Sarsgaard), who sits on Death Row, a month away from his execution date. As the two ex-partners begin looking into the cases past and present, evidence begins to suggest that a serial killer is preying on young women.

That Holder should happen to work a murder so closely matching one associated with Linden is another of those cosmic coincidences "The Killing" leans too heavily on, but there are some improvements along the way.

First, after failing to make Rosie Larsen register with the audience as anything more than a name, Sud makes a concerted effort to introduce us to a collection of homeless teens, any or all of whom could wind up as victims. Second, the action on Death Row — where Seward's sketchy behavior wins no friends among the guards(*) who are looking forward to supervising an execution — is inherently a more interesting and connected story than the election plot, especially with Sarsgaard's icy intensity. And third, the new status quo — Holder is a successful veteran detective, Linden a disgraced ex-cop with little interest (at first, anyway) in returning to the job — puts more initial emphasis on Kinnaman, whose kinetic performance was the highlight of the earlier seasons. (At one point after season 2, several media reports suggested AMC wanted to renew the series simply to keep Kinnaman attached to the channel.)

(*) Though set in Seattle, "The Killing" films in Vancouver, and the two-hour premiere alone seems to work in half of the available Canadian actors working in television, including Hugh Dillon from "Flashpoint" and Aaron Douglas from "Battlestar Galactica" as two of the guards, and Jewel Staite (most recently of "The L.A. Complex," but best-known for "Firefly") as an assistant DA. 

Some of the show's other fetishes survive intact. Our first shot is of light reflected on a rain-soaked windshield, and in a meta moment, Seward complains that his dirty cell window "Makes everything out there look murky, like you're looking through a shower glass. It's going to be this way the whole time I'm here, isn't it?" (Spoiler, Ray: yes.) And Linden's inability to maintain emotional distance from her cases has not diminished during her time away from the job: "I break things," she warns a friend.

There's a good show hiding inside "The Killing," struggling to peak out from behind the cliches and other hackery. The first two seasons suggested Sud is not the person to bring that good show out, but the first was also made in a vacuum, and the second was stuck on an unchangeable course. (Though I might have applauded if Rosie's murder had been solved in the opening minutes of the season 2 premiere before Holder and Linden moved on to something else.) This is the closest thing to a fresh start the show is going to get, and there are some promising developments here suggesting this could ultimately be a more rewarding viewing experience than "The Killing" 1.0.

The problem is that no one will know that for sure until we get to the finale — when we'll have seen whether the mystery was resolved well, whether the time spent on these characters was paid off with a deeper understanding of them, whether Sud kept relying on red herrings that make for nifty cliffhangers but make her heroes look like imbeciles, etc. — and many viewers have already been burned twice over by hoping it will feel worth it  at the end. If these episodes were the start of a brand-new series, I'd be intrigued — maybe even excited — but as a continuation of Veena Sud's "The Killing," they mainly have me waiting for the bottom to fall out. In a slow-ish summer, I'll watch for a bit to see if the show can sustain the improvements in the premiere, but the first time an episode ends with a shocking development that's immediately undone at the start of the next episode, I'm grabbing my umbrella and finding a way out of this rainstorm.

Alan Sepinwall may be reached at sepinwall@hitfix.com

NOTE: Grade is for the two-hour premiere only, obviously. More than usual, I feel this point needs to be clarified.