Unlike the disturbingly mysterious original, “Saw III” is a neatly wrapped-up package that explains everything — including Jigsaw’s evil contraptions and the background of his crazed female assistant. This strategy hardly seems the best course to sustain a horror franchise, but, with nearly everybody dead at the end — despite the hint of another sequel — pic’s 3,150-screen Halloween weekend may prove to be a whopping farewell to a stunning moneymaker for Lionsgate.

With moralistic mastermind of torture Jigsaw (Tobin Bell) set free in dubious health in “Saw II,” the new edition returns to Donnie Wahlberg’s ill-fated cop Eric having to chop off his foot to free himself from chains and irons. This marks just one of several flashbacks that eventually hinder the movie, ratcheting down its tension and pace.

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Another, even more dogged cop, Kerry (Dina Meyer), is back but not for too long, as she’s captured and killed in a diabolical contraption that rips her torso to shreds. What’s missing this time, however, is a gaming aspect that called for Jigsaw to torture only the victims he deemed worthy of punishment.

Key “Saw III” victim is ER surgeon Lynn (Bahar Soomekh), who is stressed over her failing marriage. Snatched from her hospital’s locker room, Lynn revives in Jigsaw’s lab of horrors, where Jigsaw lies close to death with an inoperable brain tumor.

Jigsaw’s high-strung assistant Amanda (Shawnee Smith) locks the usual “Saw”-esque device on Lynn, this one a neck brace triggered to detonate if Jigsaw’s heart rate flatlines. So, if Lynn wants to live, she must keep Jigsaw alive.

Unlike either first pic’s dominant, white-tiled set imprisoning two victims or the follow-up’s less effective use of a house of horrors, “Saw III” jumps from Lynn’s predicament to that of Jeff (Angus MacFadyen). Jeff is targeted by Jigsaw, rather unfairly, for wanting revenge on the driver who accidentally killed his 8-year-old son. Still-grieving dad finds himself trapped in a crate. He escapes only to find he’s in a warehouse with one of Jigsaw’s torture “games” behind every door.

Pic’s most blood-curdling scene is when Lynn drills into Jigsaw’s skull, which suggests that the franchise’s exploitative use of torture to make an aud squirmy has lost its effect.

A bigger problem lies with Leigh Whannell’s script, which utilizes so many flashbacks and explanatory inserts that the tension, a defining feature of the first “Saw,” is lost.

By the time Amanda realizes that she is the real subject of Jigsaw’s current game, another rapid flashback sequence a la “Saw II” is needed to put all the pieces together. This wrapping up of all the loose ends unfortunately leaves little that could be used to construct another sequel.

With the superb, gravelly-voiced Bell now mostly confined to a bed, more of the load is on Smith, who is not as effective in the nasty department. MacFadyen delivers a strong, almost silent performance that conveys a pained father’s dark night of the soul, while Soomekh (the distressed Iranian daughter in “Crash”) is reasonably convincing as the surgeon.

Dark, ghoulish look of “III” is identical to “II” thanks to production designer David Hackl (who also handled latter) and lenser David A. Armstrong (who has been with “Saw” since the beginning). What’s been sacrificed is the original’s distinctive use of bright lights and white sets, which ran so counter to conventional expectations in a horror pic.