Woody Allen was on some kind of a roll in the 1980s. He had already won a Best Picture Oscar for “Annie Hall” (1977), but his string of uniquely comic ’80s stories would rival any director’s of any era.

“Zelig,” a faux documentary I rewatched recently for the first time in a decade, remains one of his best, most mercurial productions. Allen stars as Leonard Zelig, a lonely man living in the 1920s who had the ability to change his appearance to fit in with his surroundings.

If he’s stuck in an Irish bar, his hair turns red and he develops a brogue. He could become black, Asian, American Indian … even overweight if he finds himself surrounded by beefy pals.

“To the KKK he was a triple threat,” intones the perfectly unctuous narrator.

I figured the film’s technological trickery would age badly. Modern F/X wizards could easily insert Allen into archival footage. But the effects on display look utterly convincing. it’s a triumph of artistic immersion, a testament to Allen’s ability to conjure up a new version of the past combined with a crackerjack special effects squad.

“Zelig” offers some big laughs along with healthy jabs at our culture, past and present. It’s one of the unsung films in his still growing canon.

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