LAST June the first season of “The Killing” on AMC ended without a bang. A gun was pointed at a murder suspect’s head, and then there was a quick cut to the credits. The explosion came later, when complaints poured in that the show had failed to solve the season-long mystery the network had advertised with the teasing slogan “Who Killed Rosie Larsen?”


In the wake of that cascade of ill will I had two thoughts. One was that if the show’s writers had wrapped up the story in that 13th episode, those same fans and critics would have complained — justifiably — that the season had been rushed and confusing and that the killer had been identified too abruptly.


The second was that if you really wanted to know the answer, or an answer, all you had to do was watch “Forbrydelsen,” the Danish show on which “The Killing” was based. It revealed who killed Nanna Birk Larsen, Rosie’s European antecedent, way back in 2007.


That’s what I did recently in preparation for Season 2 of the American show, which begins Sunday night on AMC. You can do it too, and legally, even though “Forbrydelsen” (“The Crime”) hasn’t been distributed in any format in America. A nicely packaged DVD set of the first season, with English subtitles, can be ordered online — it currently costs about $38 plus shipping from Amazon’s British site — and watched on a computer with a media player that ignores regional coding.


It’s an exercise I recommend, even if you have no interest in “The Killing.” Season 1 of “Forbrydelsen” is excellent, if conventional, television in its own right. It’s easy to understand why the show has been a hit around the world in its original form. And if you are, or were, a fan of the American series, watching its forerunner will give you a better understanding of the challenges involved in the adaptation.


The first comparison to be made between the two shows is a simple matter of mathematics. Season 1 of “Forbrydelsen” consisted of 20 episodes, each close to 58 minutes long (without commercials). Season 1 of “The Killing” comprised 13 American-length episodes of about 45 minutes each — roughly half the total running time of the Danish season.


In the course of those 13 episodes the American show departed in many details from the original. But the similarities between the two — in premise, cast of characters and broad outline of the story — were much more pronounced. Watching “Forbrydelsen” it’s clear that despite the hedging comments of the American producers, it was ordained that “The Killing” would not solve its mystery in one season, and that it would need a full second season to wrap things up.


And the division of the narrative arc into two seasons created problems for “The Killing” beyond the question of closure (which was really more of a marketing and publicity issue than a creative one).


Much of the appeal of “Forbrydelsen,” a shrewd mix of police procedural, political thriller and domestic drama, comes from its classically shaped and steadily articulated structure. Three damaged characters — a detective, a mayoral candidate and the mother of a murdered girl — are caught up in a murder investigation, and they all, for their own reasons, are trying to solve the case, in ways that lead them to stymie and hurt one another.


The mystery is absorbing and for the most part credible, but the real subject is the corrosive effect the case has on these people and their partners. (Each has one: a fellow detective, a political adviser and a husband.) As the police focus on a seemingly endless series of suspects who turn out to be innocent, the investigation comes close to destroying each of the main characters.