If you’re still mourning the loss of Leonard Cohen last month, this may help: Film Forum is screening Tony Palmer’s classic documentary Leonard Cohen: Bird on a Wire for two weeks starting January 18. A lovely antidote to all those “Hallelujah” covers, the doc follows Cohen on a month-long tour of Europe in the spring of 1972, after his salad days in New York City. While it starts off with the obligatory footage of the band boarding planes and signing autographs (Cohen was already a big deal at the time, having released his first three albums), it soon takes a far more pensive turn.

As Cohen starts off from Dublin and makes his way across 20 cities to Jerusalem, it’s clear the poet-musician has a complicated relationship with fame and performance. For the most part, he’s an open book. He even lets Palmer– a Brit known for his Zappa film 200 Motels and other rock docs– film him while he’s swimming and showering naked. With his trademark self-deprecation, the singer, 37 at the time, gamely fields even the most asinine questions from European journalists. “Can you stand Leonard Cohen for more than half an hour?” one of them asks, alluding to the idea that Cohen’s songs are suicidally dark and depressing. Cohen just grins and answers, “Oh, nowhere near that long.”

Cohen’s self-effacing nature went over famously well with women, and more than one of them throw themselves on him backstage during the course of the tour. “It’s hard to come onto a girl in front of a camera,” he says to one of them while trying to figure out how to arrange a meeting with her, despite the scowling man at her side. He puts off another woman who wants to take him to “a place” in Tel Aviv: “I feel like I’m going to disgrace myself tonight, so I hate to make an appointment.”

It isn’t all suaveness and bedroom eyes. Cohen’s ambivalent attitude toward fame can be seen as he prepares to sing “Suzanne,” and tells the audience that he’s glad the rights to the song were “stolen” from him– “because it would be wrong to write this song and get rich from it, too.” The audience cheers, but there’s a twinkle of resentment as Cohen talks about the “friend” who ripped him off.

Cohen often introduced his songs with such prologues (a great many of them are preserved online), which is indicative of his intimate relationship with his audience. During his performances, we see him inviting the crowd to sit closer and even onstage, and telling security guards to lay off. But it wasn’t always a love-in. In West Berlin, before starting into “Avalanche,” he tells some unruly types in German, “Do you want total war?” In the Netherlands, the sound system craps out and some angry Dutchmen accuse Cohen of scamming them. He refunds their tickets out of his own pocket, but to no avail.

Toward the end of the tour, that sound system proves to be a headache, and Cohen at one point delights the crowd with an impromptu ditty about wanting to take an axe or some dynamite to it. But the technical difficulties are just part of his frustration with performance. He complains to one crowd about having to play “museum songs” that were written for a certain woman years ago. “I wanted to tell one person one thing and now I am in a situation where I must repeat them like a parrot chained to his stand, night after night,” the self-described “broken-down nightingale” complains.

For Cohen, performance was a two-way street, and he often found himself breaking down in the middle of it. In an interview, Cohen tells a journalist that “you don’t want to go in front of people unless you feel you can give them something and you can return to them the love that they feel to you, through your songs.” That anxiety culminates during the tour-end show in Jerusalem, where Cohen, citing a passage from the Kabbalah about Adam and Eve, tells the crowd, “Somehow the male and female part in me refuse to encounter one another tonight and God does not sit on his throne. And this is a terrible thing to happen in Jerusalem.” He heads to the dressing room to “profoundly meditate,” but then decides that maybe it’s just a good shave that he needs.

While Bird on a Wire definitely peers deeper into Cohen’s psyche than, say, Don’t Look Back did into Dylan’s, it’s the songs that shine here. The end of the tour leaves Cohen is in tears backstage, and there’s a good chance you’ll be in the same state at the end of this film.

“Leonard Cohen: Bird on a Wire,” January 18-31 at Film Forum, 209 West Houston Street; daily screenings at 12:30, 2:45, 5:10, 7:25, and 9:45.