A little boy with knowledge and powers beyond his years — actually, beyond his species — goes on the lam with his father in “Midnight Special,” a moody science-fiction thriller from writer-director Jeff Nichols (“Take Shelter”). Mixing the paranormal premise of “Firestarter” with the conspiracy-fueled paranoia of “Close Encounters of the Third Kind,” the film has a cornucopia of good ideas and many shivery scenes, but never adds up to a completely convincing story.

Its star is Jaeden Lieberher, the wisp of a boy who held his own opposite Bill Murray in 2014’s “St. Vincent” and subsequently charmed America by wearing suits and bow ties on the red carpet circuit. Lieberher plays Alton, who we first see wearing dark goggles and runway-caliber ear mufflers while draped in a bedsheet. He’s a quiet, frail kid, but the way the grown-ups treat him — with tenderness and a touch of caution — tells us that the protective headgear is for everyone’s good.

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Alton and his father, Roy (an understated Michael Shannon), are fleeing from police, the FBI, the NSA (represented by Adam Driver as a nebbishy number cruncher) and religious zealots from a Texas compound called The Ranch (shades of Waco, with a silver-haired leader played by Sam Shepard). How Alton got into this mess takes a little explaining. The back story is awfully contrived — we can tell it took some doing to arrange this story just so — but Nichols deftly weaves the exposition into the dialogue.

For the most part, “Midnight Special” unfolds skillfully, building a sense of tingly dread as it parcels out clues to Alton’s remarkable techno-spiritual abilities: He can eavesdrop on satellites, control computers and give people indescribable visions. Joel Edgerton plays a convert, Lucas, who protects Alton with dogged loyalty; Kirsten Dunst plays Sarah, who knows that Alton is more than just her little boy.

When all is finally revealed, detail-oriented viewers may feel a little let down. In the end, the movie’s questions are more fun than its answers.