It may be more “Fail Safe” than “Dr. Strangelove,” but Gavin Hood’s “Eye in the Sky” is a nifty little thriller, though one drawn on a far smaller scale than either of those nuclear-destruction visions of the sixties. The doom in this case will be confined to a single block in Nairobi that’s in the control of Al-Shabaab militants, and the explosive device will be a missile fired from a pilot-less American drone. But as imagined by scripter Guy Hibbert, the kinds of political and military arguments that take place over the decision to attack the target might remind you of the harangues in Kubrick’s war room—though without such blatantly comical thrusts.

The set-up finds no-nonsense British Col. Katherine Powell (Helen Mirren) planning her final move in a long-gestating plan to capture an English-born radical named Susan Danford (Lex King), who’s in league with the Somalian terrorists, while she confers with them in Kenya. Powell has on the line her superior Lt. Gen. Frank Benson (Alan Rickman), who’s surrounded by a tableful of government ministers and their political advisors; a Kenyan commander (Babou Ceesay) ready to send in shock troops to make the arrest; and American drone operator Steve Watts (Aaron Paul) who’s providing the titular mode of moment-by-moment observation that makes the operation feasible.

Things ratchet up a notch when two young radicals, one British and one American, show up in Nairobi and join the conspirators. That leads to calling in undercover Kenyan agent Jama Farah (Barkhad Abdi) to put his safety in danger by getting close enough to the house where they’re all meeting to send in a smaller version of the drone—a plastic insect with an embedded camera—to buzz inside and see what exactly is going on. It turns out that the two youngsters are being fitted with suicide vests and automatic weapons. Suddenly the mission changes from one directed toward capture to one that involves bombing the place.

There’s lots of discussion about whether such a change can be approved—legal niceties and public perceptions become matters of dispute as Powell grows increasingly anxious that the targets will fly and untold victims will die. As the dithering among Benson’s unwelcome guests (who include Jeremy Northam as a wavering minister, Richard McCabe as a legal advisor and Monica Dolan as a political consultant) continues, Powell has to deal with frustrating advice from her own consultants—risk assessment advisors and legal staff—as well. Ultimately the decision is repeatedly kicked upstairs—all the way to the British Foreign Secretary (Iain Glen), who’s suffering from an embarrassing episode of food poisoning during a trip to Singapore, and even to the US Secretary of State (Michael O’Keefe), who interrupts a ping-pong game in China to brusquely bark his approval.

And a new element enters the equation when a little Kenyan girl (Aisha Takow) sets up her bread-selling table immediately beside the target house. Her presence leads not only to additional assessments of acceptable collateral damage—would it be more politically palatable for the terrorists to be blamed for hundreds of deaths than for the British government to be held accountable for that of a single innocent?—but also to requests from the drone pilot to minimize the possibility of the girl’s death. That leads Farah to put himself into even greater jeopardy in order to get the youngster out of harm’s way, and Powell to finesse her team’s assessments in order to get permission to strike.

To some extent “Eye in the Sky” serves as a complement to Andrew Niccol’s “Good Kill,” in which Ethan Hawke played a drone pilot who had to make difficult choices at the job. While Niccol’s film was deeply serious, however, Hood’s—though it raises provocative issues in an essentially dramatic way—is shot through with moments of very dark humor. The action, both in the field and in conference rooms, is crisply staged by Hood on South African locations, and paced for maximum tension by cinematographer Haris Zambarloukos and editor Megan Gill. Production designer Johnny Breedt also deserves credit for fashioning convincing interiors on an obviously limited budget, while the special effects supervised by Mickey Kirsten and the score by Paul Hepker and Mark Kilian add to the menacing mood.

The cast is impeccable. Mirren is a model of steely determination, and the late Rickman, in one of his final roles, is typically suave, pulling off even a minor subplot about buying a doll for his daughter and a final face-off with Dolan. Second-billed Paul is fine if unremarkable and Abdi (from “Captain Phillips” is excellent, but it’s the secondary cast—particularly Glen, Northam and O’Keefe—who add the most memorable touches.

“Eye on the Sky” won’t be a breakout hit any more than “Good Kill” was. But those who seek it out will find a tense, tough, biting commentary on the way wars are fought today.