Joel Kinnaman and Mireille Enos

Joel Kinnaman and Mireille Enos star in "The Killing," premiering Sunday on AMC.

In today's TV world, the most popular crime dramas have an extraordinarily high body count, racking up one or more victims an episode and then starting over the following week with more casualties and a new investigation.

Starting with a two-hour premiere on Sunday, April 3, on AMC, "The Killing" follows, over the course of 13 total hours (with each hour representing roughly one day), a single murder.

Not surprisingly, it's based on a concept from a nation where murder is much less a part of the psyche and daily reality. "The Killing" is based on the hugely successful Danish crime series "Forbrydelsen" (meaning "The Crime"), which follows one incident over the course of a season.

Veena Sud ("Cold Case"), the writer and executive producer of the American version, says, "We live in a society that is incredibly violent, and much more violent than Denmark. Amber Alerts are the norm on the highway, and a missing child, a missing teenager in a major American city never makes the news.

"So the biggest challenge was to make us, as Americans, care about this young girl over a very long course of time."

Mireille Enos ("Big Love") stars as no-nonsense homicide detective Sarah Linden, who catches a case on her last day of work in Seattle (the show shoots in Vancouver, Canada) before moving to California with her son (Liam James) and fiance (Callum Keith Rennie).

Rosie Larsen, a promising high-schooler from the wrong side of the tracks, has gone missing, and when she turns up dead, the evidence points to city council president Darren Richmond (Billy Campbell), a fast-rising politician with mayoral aspirations.

The news shatters the girl's parents, Mitch and Stanley (Michelle Forbes, Brent Sexton), who still have younger sons to care for, and also shakes Rosie's friend, Sterling Fitch (Kacey Rohl).

Working with Sarah on the case is former narcotics detective Stephen Holder (Joel Kinnaman), who has a dark sense of humor and an unconventional investigative style.

As for how she saw Sarah, Enos says, "I saw her as intelligent, complicated. She can be really cagey. She can set up boundaries between herself and other people. She keeps people at bay. She's not always likable, which is really fun to play."

Although Campbell plays a politician, he says, "I don't know that I'm a slimy politician at all. He seemed a very decent man. He still does seem a decent man. He's in for a bit of, maybe, an object lesson in what it means to be a politician. He's going to find out some things about himself.

"It's pretty neat to be on a show with actual character arcs. It's exciting."

Because the show moves along day to day, it allows the actors to dig into scenes and feelings that would normally be skipped over quickly.

"That's the really beautiful thing about this show," says Campbell. "You do live with these people through their experience, almost in real time. It's stunning."

It also allows the victim to become more than just a reason for a clever detective to get to work.

"The most important thing was not to pornographize murder," says Sud, "and to see the real cost and the real toll when a child is lost. We're not spending time looking at a dead child's body and just analyzing that; we're spending time with all the people who have lost her and (seeing) the impact of this loss on her mother, on her siblings, on her father.

"Every episode is a day, so you are seeing every day what happens in the moments and the hours and the days after you've lost a child -- what it's like to pick out a dress, what it's like to identify your daughter at the morgue, what it's like to make breakfast for her younger brothers the next morning; what do you tell them?

"When I was doing research for the pilot, I spent a lot of time with parents who had lost their children, expressly for the purpose of telling this story in a way that was authentic and respectful. A lot of television isn't about murder victims. What I heard over and over again was not, 'Don't tell our story,' but 'Tell our story in a truthful way.' "

For Enos, who was four months pregnant during the pilot and was later shooting the show as a new mother, it was especially emotional.

"I didn't actually feel it during my pregnancy," she says. "I was able to keep distance from it, but now that my daughter -- my first baby, a little girl -- has been born, I definitely have had some very hard moments shooting, watching Michelle.

"She's so incredible to watch, and the places that she goes, I'm thinking about my own daughter. It's been tough."