Readers took their time finding Kent Haruf, but he was a patient man who didn’t care much for the trappings of fame anyhow. His popularity swelled quickly, though, when he published his third novel, “Plainsong,” in 1999 at the age of 56. The book was a bestseller for months and a finalist for the National Book Award, which meant he had to dress up for the ceremony in New York and wear a medal on a ribbon around his neck and feel genuinely uncomfortable. Afterward, he told the New York Times, “We’re nuts, crazy in this country about fame. We expect writers to be something between Hollywood starlet and a village idiot.”

By the time he died last November at the age of 71, he had successfully avoided either of those fates and published five quiet, beloved novels about the people of Holt, Colo., a fictional town drawn from his itinerant adolescence. In his obituary, there was mention of a manuscript he’d completed just before dying, and now we have a chance to read that final book. Such posthumous publications come trailing clouds of skepticism, but “Our Souls at Night” is such a tender, carefully polished work that it seems like a blessing we had no right to expect.

The novel opens with a sentence as simple as a line from the Gospels: “And then there was the day when Addie Moore made a call on Louis Waters.”

That initial “and” is a modestly brilliant touch, an assumption that we’re already involved in the lives of these people, already waiting for the next — and, alas, last — installment about Holt, Colo. The story that quickly develops follows Addie and her neighbor Louis. Both live alone, nursing memories of doleful marriages they stuck with until illness stole away their spouses. Neither has any reason to expect the remaining years will offer relief from the arid rituals of retirement in a small town. Indeed, what older folks are allowed to expect from their lives becomes the central theme of this slim but never slight book.

When Addie knocks on Louis’s door, he knows her only as the widow of a local insurance salesman. He invites her to sit in the living room, and after a few sputtering starts, she make an outlandish proposal: “I’m lonely. I think you might be too. I wonder if you would come and sleep in the night with me.”

Half-a-century after the sexual revolution, in the shame-free age of Tinder, Blendr, Grindr et al., it’s funny how bold Addie’s proposal sounds. Decent folk know that old people are supposed to live lives of resolute solitude to protect their dignity (and our inheritance). When the time comes, we’ll move them to an institution where they can be tended by cheery strangers until they pass away in drugged incoherence.

But for some reason that modern pact doesn’t appeal to Addie. She’s tired of her isolated life and particularly of those long nights, but she has no intention of checking out early. Instead, she’s devised a solution: “I think I could sleep again if there were someone else in bed with me,” she tells Louis. “Someone nice. The closeness of that. Talking in the night, in the dark. What do you think?”

That’s a question not just for Louis, but for us. After all, we live in a culture fiercely intolerant of any articulated prejudice except ageism. Popular entertainment spews out stereotypes about older people and their cloying desire for companionship. And if the possibility of sex in the golden years isn’t being entirely ignored or derided for comic effect, it’s being announced on magazine covers like the discovery of levitation.

Addie and Louis know all this, but they’re determined to make one last attempt at happiness even at the risk of scandalizing their adult children and town busybodies. “I made up my mind I’m not going to pay attention to what people think,” Addie says. “I’ve done that too long — all my life. I’m not going to live that way anymore.” And so she waits while Louis gets his hair cut, takes a long hot shower, trims his fingernails, packs his pajamas in a paper bag and walks over to her house. “I don’t know how this will go,” he confesses.

How it goes is utterly charming. Watching Addie and Louis tiptoe into this self-conscious plan for intimacy is a pleasure. They’re nervous as teenagers, unsure about what they’re up to and what they can expect from each other, but they possess the wisdom and kindness of long, contemplative lives. “I don’t know if I’ll be able to sleep tonight,” Louis says. “I’m too keyed up.” It’s impossible to resist the thrill these two sweet people feel as they get to know each other night after night.

This isn’t a traditional romantic comedy — that is, it doesn’t end in marriage — but it’s wonderfully romantic and, for a time, comic. It’s delightful to see Haruf having some fun with these two — and even engage in rare moments of autobiography and metafiction. At one point, Addie and Louis talk about a Colorado novelist who writes books about Holt County. “He could write a book about us,” Addie says. “I don’t want to be in any book,” Louis responds.

But those sweet moments of humor are subsumed in the poignancy of the stories they tell each other every night. Clothed in darkness, Addie and Louis can finally speak of their failings and disappointments, the losses and tragedies that break and reset our bones. “Life hasn’t turned out right for either of us,” Addie says without a hint of self-pity, “not the way we expected.”

“Except it feels good now, at this moment,” Louis reminds her.

There’s a little more action, to be sure, including some unkind gossip and family opposition that these two new old friends must contend with, but, in a sense, Addie is right when she says, “It’s just two old people talking in the dark.” In Haruf’s spare sentences, though, it’s a lot more than that. He’s working within the tight boundaries of two lives that don’t much matter in a small town that has never mattered, but he makes everything seem consequential with his unadorned style. Perhaps more so than any of his previous books, the language of “Our Souls at Night” is distilled to elemental purity. Most of the novel consists of dialogue without quotation marks; the narrator’s light descriptions are factual and tone-free. Any particular line may sound flat, even colorless, but the cumulative effect of these Shaker sentences is absorbing and reverent.

Toward the end of “Our Souls at Night,” Louis says, “I just want to live simply and pay attention to what’s happening each day,” which probably comes pretty close to what Haruf wanted, too.

Ron Charles is the editor of Book World. You can follow him on Twitter @RonCharles. For more books coverage, go to washingtonpost.com/books.

On June 25, Kent Haruf’s editor, Gary Fisketjon, will be in conversation with The Washington Post’s Mike Rosenwald, a former student of Haruf’s, at Politics & Prose Bookstore, 5015 Connecticut Ave. NW.

OUR SOULS AT NIGHT

By Kent Haruf

Knopf. 179 pp. $24