THE LAST time AMC adapted a comic book for television, the result was a little show called “The Walking Dead.” So the network gleefully returns to blood-soaked comics as source material, hoping for another high-body-count hit with “Preacher,” which made its debut Sunday.

When adapting comics, AMC steers clear of capes and secret identities — the sort of superhero fare seen on the CW network and Netflix. For “The Walking Dead,” AMC turned to Robert Kirkman and Image Comics — a cartoonist and publisher known for mature, creator-owned content that rolls much harder than some PG-13 Spandex. Now, with “Preacher,” AMC has turned to Vertigo — DC Comics’ mature-content imprint — to adapt a classic hit created by Garth Ennis and Steve Dillon in the 1990s.

The new show is under the influence of the comic, but if you haven’t read “Preacher,” you won’t feel lost. A preacher comes across a great and strange and scary power and suddenly has an eerie influence over his flock that he never had when he initially tried to follow in his late father’s religious footsteps. There’s also a crazy vampire and a seemingly even crazier ex-girlfriend of Preacher’s — and they form an unlikely trio headed for who-knows-where.

Dominic Cooper — whom Marvel fans will recognize as a young Howard Stark — stars as Jesse Custer, the preacher who’s trying to lead a church more out of grief and obligation than his own religious fervor. Here, the British actor speaks with a less-than-convincing, still-entertaining twang. Cooper is not going to convince you that he’s a Texan, but he does possess a certain menace on-screen.

And “Preacher” has its moments. Cooper is always entertaining, but the series premiere plays it safe. I think a Vertigo-comic-adapted show would be a better fit on a no-holds-barred network such as HBO or Showtime. But a few scenes help “Preacher” merit its 10 p.m. time slot. Enough goes down to get us caught up in this universe, and crazier things are hinted at by episode’s end.

If “Preacher” wields any larger power, it could lie in its ability to convert other networks — to make them realize there is an untapped treasure-trove of mature, non-superhero comics worth converting to television. If “Preacher” can lead us to adaptations of such comics as “Y: The Last Man” and “American Vampire,” then it’s done good work in these parts.