Matthew Heineman covered one aspect of the Syrian Civil War—the ISIS takeover of the city of Raqqa in the north, and the attempts of refugees to alert the world of the horrors being perpetrated there—in his documentary “City of Ghosts.” He now expands his work to remind us again of the cost of the Syrian conflict, and of others as well, through this biographical film about American-born, London’s Sunday Times war correspondent Marie Colvin, who died covering the siege of Homs by the forces of Bashir al-Assad in 2012.

Rosamund Pike delivers a strong—some would say frantic—turn as Colvin. Arash Amel’s script, based on a Vanity Fair article by Marie Brenner, tells us virtually nothing of the reporter’s earlier life, dropping us into her career a little over a decade prior to her death, when her insistence on covering the rebel Tamil Tigers in Sri Lanka by joining rebel forces—a dangerous tactic resisted by her long-suffering editor Sean Ryan (Tom Hollander, nicely combining a harassed air with a professional desire to get the story)—results in the loss of sight in her left eye, but her celebration by colleagues in the media.

Her recovery is difficult but she insists on continuing reporting from dangerous war zones, and the film follows, year by year, her harrowing experiences—among them near Fallujah in Iraq, where she joins forces with photographer Paul Conroy (Jamie Dornan) and a local reporter (Fady Elsayed) to document the exhumation of the remains of Kuwaiti POWs in a mass grave; in Libya, where she interviewed Qaddafi and witnessed his fall; and finally in war-torn Syria, where she and Conroy suffered through intense bombardment along with the rebels in Homs, electing not to leave in order to continue to send reports in a decision that led to her death.

Throughout Colvin is portrayed not as some plaster saint, but as a deeply troubled woman whose friend Rita Williams (Nikki Amuka-Bird) points out that she appears to be suffering not only from post-traumatic stress (for which she eventually seeks treatment) but from alcoholism. The film emphasizes how haunted she was by the horrors she had witnessed, including the death in Libya of another war correspondent, here called Norm Coburn (Corey Johnson), and those of children killed or wounded in airstrikes and roadside bombings. And yet it never undervalues her idealism to the cause of making the world aware of the suffering it chose largely to ignore in the Arab world, and her unequivocal determination to serve that cause despite the threat it posed to herself, as she explains to a young colleague (Faye Marsay) who is not quite so committed to following in her footsteps.

Less attention is devoted to Colvin’s personal life, though the early scenes portray her frayed relationship with her ex-husband (Greg Wise) and later ones her romance with a fund-raiser named Tony Shaw (Stanley Tucci, who brings his customary smoothness to a thankless part). The impression—which seems a correct one—is that Colvin was obsessed with her job to the near-exclusion of all else, but tried desperately, during her times back home, to “forget” what she had seen and heard in the field by partying and drinking heavily. One might be tempted to criticize Colvin for taking incredible risks to tell a story that was, as she put it, the first draft of history, but “A Private War” helps you feel how her fanatical, life-endangering sense of mission was fueled not by egotism or self-importance, but by the ghosts of the man-made horrors she had witnessed.

There’s no question that “A Private War” represents an intensely important a story for Heineman to tell, just as Colvin’s war coverage was for her. (In addition to “City of Ghosts,” he also made “Cartel Land,” about Mexican civilians who banded together to fight local drug dealers.) Like her, he is clearly infuriated with the refusal, or inability, of governments to intervene in places where people are being brutalized and killed and take action to stop the violence. His medium puts him in less danger, of course, but the intent—to raise awareness—is similar.

That’s a noble purpose, and his film is a good one—boasting an incisive script, a fine cast with an especially committed lead, and solid work from a technical team—particularly production designer Sophie Becher and cinematographer Robert Richardson—that was probably working on quite a limited budget. While presenting an honest, warts and all portrait of a woman so driven to inform readers of the mad violence in the world that it cost her her own life, however, it will probably suffer the fate of most well-meaning films designed to be both pointed drama and spur to action: it will be seen by relatively few.

That’s a pity, but it’s the way things are nowadays.