It’s an uphill battle, but Dan Klores and Fisher Stevens seem up for the challenge: to take a New York story that played out for years in the public arena and craft a documentary that seeks to find some new life in the story.

Most big-screen documentaries strive to focus our attention on a subject or an issue that’s never quite broken through to the mainstream. Hubert Sauper’s 2004 documentary “Darwin’s Nightmare,” perhaps the last great film of its kind, found a story about ecological destruction in Africa that captured many of the ways in which Western capitalism has poisoned and pillaged communities and countries in the Third World. “Romantico,” one of last year’s finest docs, offered a glimpse at the life of two illegal immigrants in San Francisco and was far more intimate than anything to be found on a nightly news broadcast.

Yet the tale that made “Crazy Love” possible was front-page news, if sporadically, during a span of some 50 years. In 1959, a 32-year-old Bronx lawyer named Burt Pugach hired three thugs to attack his 22-year-old mistress, Linda Riss, ordering them to throw lye in her face. The attack, which Pugach orchestrated after Ms. Riss dumped him and became engaged to another man when he repeatedly broke promises to divorce his wife, left the beautiful young secretary scarred and blind. As the incident became public and the city’s tabloids pounced, a splashy trial — in which Pugach defended himself and eventually slit his wrists in the courtroom after pronouncing his love for his victim — served as something like catnip for crime editors and headline writers who cherished every twist and turn.

But, as those who followed this story already know, the most bizarre details were yet to come: Pugach, serving 14 years of a 30-year sentence, swore from behind bars that he still loved Linda, and when he was released in 1974, she agreed to marry him (“He was the only prospect I had, let’s put it that way,” she later said).

It says something about the high caliber of today’s documentaries that the first half of “Crazy Love” feels overlong and underwhelming. In the old days, hit men throwing acid into a woman’s face on the orders of her jealous older lover would have been juicy enough for an entire novel. But in “Crazy Love,” those unfamiliar with the infamous attack may wonder why the subject is worthy of a feature-length dramatization.

That’s not to question the thoroughness of the directors’ reconstruction or the surreal nature of the story, but rather the pacing of the drama as it’s seen here. Many viewers will have to wait 40 or 50 minutes before they can pick their jaws up off the floor, but it isn’t until the final bit of interviewing that “Crazy Love” takes the conversation somewhere more universal than the pun-filled news coverage one could find by Googling the topic.

Offered remarkable access, the directors interview Burt and Linda personally and openly in the their Queens apartment, along with their family and friends, the editors who managed the story as it unfolded, and even the television interviewer who was dumbstruck to find Pugach proposing to his victim on the air in 1974. With all this material, we get a crystal clear picture of who these two were, in times both good and bad.

Perhaps it would have been more interesting to start with the bad, since that’s precisely what makes the good so unlikely. How could a woman love the man who blinded and deformed her? Why did a man convicted of such a crime think that he could ever win back her heart? As constructed by Messrs. Klores and Stevens, the film’s systematic, somewhat plodding progression from picture-perfect romance to gruesome crime caper lacks the punch that a story this unique and bizarre — not to mention perverse and even uplifting — deserves.

For at its end, “Crazy Love” careens toward an unforgettable conclusion that is at once cynical and honest: Did Burt and Linda turn to each other late in life because, being a blind woman and a publicly reviled ex-convict, they had no one else? Or was it because these two, who were passionate lovers, enemies, and then lovers again, had seen both the best and worst of each other, and had been unable to deny their love any longer?

As they walk through the experiences, there’s clearly a great deal of pain: Burt’s bravura stalls when he discusses the attack, and Linda still resents the way her engagement fell apart after her disfiguration, and how she suddenly found herself alone and confused. But as they recall their more recent experiences together, another sentiment surfaces. Seeing the two together in the present, there’s something at once uncomfortable and refreshing about their candor with each other — the kind of bluntness that can only emerge when two people have seen each other at their worst.

Forgoing what the Bible says, sometimes love is indeed mean and callous and difficult to understand. Maybe Burt and Linda aren’t the poster children for love, but maybe love is something that casts aside our logical senses and renders us servants to something we don’t understand. If these two damaged souls can love each after all this, then anyone can love anyone.