After innumerable remakes, sequels, prequels and just plain ripoffs, “Texas Chainsaw 3D” returns to the story of Leatherface by pretending that none of them ever happened and jumping off from the ending of Tobe Hooper’s 1974 original. It also offers a story that’s far more developed than most slasher fare. But the result is a picture unlikely to satisfy either fans who feed on the yucky, in-your-face blood-and-guts overkill of the slice-and-dice genre, or the more discerning filmgoers who saw a subversive social commentary in the original.

After a prologue that shows the Sawyer family—presumably including chainsaw-wielding Leatherface, aka Jed (Dan Yeager)—wiped out by a mob that torches their house and sprays it liberally with bullets, we learn that an infant had been rescued from the melee and raised by a white-trash couple that quickly leaves the little town of Newt, Texas (which, given that the sheriff’s cars identify them as belonging to Fannin County, must be somewhere near Bonham).

A couple of decades later the baby has grown into a babe—Kristin Miller (Alexandra Daddario), who’s living with handsome dude Ryan (Tremaine “Trey Songz” Neverson) and is shocked to learn she’s adopted when a letter arrives informing her that her grandmother has died, leaving her the heir to the family estate. Soon she, her boyfriend and another couple, Nikki and Ryan (Tania Raymonde and Keram Malicki-Sanchez) are off to New Orleans in their van, planning to stop briefly at Newt to check on the house. Along the way they pick up charming hitchhiker Darryl (Shaun Sipos). Of course, the stay is longer than they expect—or, for most of them, shorter in terms of enjoying the place. Because it turns out that grandma’s house isn’t totally unoccupied, and its resident doesn’t take kindly to unwelcome visitors (something that Heather could have learned immediately had she bothered to read the letter the deceased old lady left for her).

What follows, of course, is a series of killings, though to be honest, until a big splurge in the final reel, director John Luessenhop mostly eschews the orgy of splatter effects that have become obligatory in this genre since the torture-porn of the “Saw” and “Hostel” franchises. (Heck, the movie is so decorous early on that after a street-level establishing shot of a dead armadillo on the pavement, it doesn’t show the beast being squashed by the tires of the passing van, but has them carefully swerve by the critter. And a scene in which Leatherface chases a potential victim into a crowded carnival is played more for laughs than shocks.) Luessenhop also thankfully forgoes the jerky, hyperactive camera style so commonplace in these kinds of flicks nowadays; together with cinematographer Anastas Michos he opts for steady, well-composed widescreen images, and even holds the obvious 3D moments to a minimum, thrusting blades into our eyes only occasionally.

All of that will probably disappoint those looking for more gore, who may also think that the movie is overloaded with plot. Not since Richard Franklin’s “Psycho II” (1983) has a script tried to follow some logic (garbled and riddled with holes though it might be) in continuing the story of an iconic madman in what amounts to an attempt to rehabilitate him. (One of Leatherface’s actions involving a grave even calls Norman Bates’ mother fixation to mind.) You have to give scripters Adam Marcus, Debra Sullivan and Kirsten Elms credit for doing something different from standard slasher fare in concocting a story that wants to make Leatherface, of all people, a sympathetic—even heroic—figure. But it’s a stretch to try to make that jibe with the portrait Hooper drew of him nearly four decades ago, and no message about family ties can wipe away all the blood that’s been spilled over the years.

While the new “Chainsaw” may be superior to most such fare in writing and direction, moreover, the acting remains pretty poor. Daddario’s main positive attribute is a well-toned midriff, which costume designer Mary McLeod assures is visible pretty consistently, and Raymonde does her slutty routine adequately. The guys are blander, with rapper Neverson showing off a buff physique but not much more, though Sipos exudes a raffish charisma. Paul Rae overdoes the Texas bit as Newt’s on-the-make mayor with a guilty secret, while Scott Eastwood is a handsome cipher as an ostensibly helpful young cop.

In sum “Texas Chainsaw 3D” isn’t as bad as you’d expect—it’s certainly a step up from previous 3D horror remakes like the “Piranha” flicks or “My Bloody Valentine”—but it’s further evidence that the kindest cut would be to leave these old movies alone.