I’ve been wondering for years why no one has ever made a good Mossad movie. From The Little Drummer Girl (1984) to Munich (2005) to awkward fictions in between, Hollywood has never managed a portrayal of the Israeli secret service that gets beneath the surface of the organization or its people—nothing approaching the gold standard set by the BBC’s masterpiece Tinker, Tailor, Soldier, Spy (1979) about the British MI6 in the cold war.

By contrast, the Hollywood rendition of Israeli spy action, shoehorned into various genre clichés, tends to involve shooting people and/or blowing them up, interspersed with interludes of Jewish moral discomfort. “I’m proud of what you’re doing,” an Israeli mother says to her son, the Mossad agent Avner in Munich, to which he replies unhappily, “You don’t know what I’m doing.”

I therefore watched the new Netflix series The Spy with low expectations. It was hard to imagine that the series’ star, the outrageous British comedian Sacha Baron Cohen, could possibly do justice to what is perhaps the great triumph and tragedy of Israeli intelligence: the story of Eli Cohen.

That true-life spy, the son of a Syrian-Jewish family who grew up in Egypt, arrived in Syria in 1962 using the cover identity of a Syrian Muslim businessman from Argentina named Kamel Amin Thabet. He made important friends and began radioing information to his handlers in Tel Aviv, including descriptions of Syria’s deployment on the Golan Heights, which Israel would capture in June 1967.

But Cohen wasn’t around to see that event, because two years earlier Syrian counterintelligence received new Soviet equipment that allowed them to pick up his transmissions. Soldiers burst in on him as he transmitted on his Morse set. The Syrians hanged him before a crowd in Damascus in May 1965.

The flaws of The Spy are easy to spot. The great Israeli comic actor Moni Moshonov is utterly miscast as the intelligence chief, inexplicably playing the spymaster as the kind of nebbish who’d be running a kibbutz kitchen. The script, delivered in English with a sort-of Israeli accent (including, a bit disconcertingly, by the American actor Noah Emmerich as the spy’s handler), sometimes sounds as if it were actually written by not-quite-native English speakers working off a list of clichés. “I thought we stopped doing that,” the Emmerich character says when his sultry female sidekick propositions him during a late night at the office. “Desperate times call for desperate measures,” she says. Yes, that is what she actually says.

It would also be easy to dissect the historical flaws, of which there are many. Cohen wasn’t really friends with President Amin el-Hafez, for example, and there’s no evidence he ever met the famous Ba’ath-party ideologue Michel Aflaq. But that kind of quibbling would miss the point, especially since the show doesn’t claim to be faithful to history. The surprising fact is that The Spy actually works. It held my attention, made me feel for the characters, and made me dread the end even though it was never in doubt.

Much of the credit goes to Baron Cohen, who somehow caused me to forget his comic incarnations as the hip-hop wannabe Ali G, the Kazakh journalist Borat, and the flamboyant Austrian fashionista Bruno. Some of his past performances have been brilliant, and many have been lewd and juvenile. You might remember, no matter how hard you try not to, the stunt at the 2009 MTV music awards in which Bruno landed in Eminem’s lap wearing wings and a spangled jockstrap.

In his role as Eli Cohen, however, Baron Cohen summons new talents. He manages not only to convince as the doomed agent but to suggest a credible explanation for his success, one I hadn’t thought of until now: a charismatic, even gregarious personality. I’d always imagined Eli Cohen as sophisticated and quiet. But to have had so many friends, he must have been someone you wanted to be friends with. That’s how Baron Cohen plays him, with a wink and a broad smile: a man who fills the room, who’s quick with a hug, a joke, or a genial bribe.

The other striking performance is that of Hadar Ratzon Rotem as the story’s second hero: Eli’s wife Nadia, left alone in a tough country with young children, unaware of what her husband is up to. (She’s told he’s an acquisitions representative for the defense ministry.) Nadia comes across as sympathetic and tortured, and it’s hard to bear the news that you know is coming.

Hollywood’s Mossad movies haven’t been good in part because most Western observers have never really grasped Israel’s secret identity, which is also the secret that made the Mossad’s reputation in its first decades. This is the fact that more than half of the new state’s population came, like Eli and Nadia, from the Arab world and included people who could move in that world with ease, as Arabs. That fact has been obscured by Israel’s own Europe-heavy narrative, by the West’s Holocaust fixations, and by the Mossad’s own PR about derring-do and technical wizardry.

The truth is that Mossad recruiters had at their disposal an invaluable reservoir of people who were loyal to a fault, ideologically motivated, and capable of passing for the enemy. One of them was Eli Cohen. There were many others who, unlike Cohen, remain anonymous because they were lucky enough to make it home.

The series deserves credit for broaching, if only in a peripheral and inelegant way, the harsh ethnic irony of the Cohens’ life: namely, that the same characteristic that made Eli useful to Israel’s young intelligence service was what kept his family on Israel’s margins. Being an Arabic-speaking Jew in those years was useful if you were a spy. In real life it was a handicap to be overcome.

“You know what they see when they look at me?” Eli says to Nadia after a party at the poolside mansion of Ashkenazi friends, where the host mistakes Eli for a waiter: “They see an Arab. That’s it. Jewish, yes. But just an Arab.” Never mind that no such mansion could have existed in socialist Israel circa 1960, or that the host’s 1970s shirt and haircut are off by at least a decade. Eli’s point to Nadia gets at something true, and if there are to be more—and better—Mossad stories told on screen, they’ll have to address it again and in much greater depth.