“Koch” opens Friday at Sundance Cinemas. Not rated, 1:40, three stars out of four.

Ed Koch, the recently deceased mayor of New York City, was a man of contradictions so obvious that he must have secretly reveled in them. He was an arrogant man who famously asked everybody “How’m I doing?”, a man who could be generous and gregarious with crowds but petty and arrogant at the one-on-one level. Even at the end of his life, his politics were tricky — supporting of same-sex marriage, opponent of the so-called “Ground Zero Mosque.”

Forget “A Tale of Two Cities:” — the documentary “Koch” is a tale of two mayors. At least two.

Neil Barsky’s first film does an entertaining job capturing the many facets of Ed Koch — or at least as many as Koch has ever been willing to reveal to the world. Barsky keeps the focus almost exclusively on Koch’s three terms as mayor in the 1980s, how his tenure both revived the strengths of the city he loved as well as exposed its flaws.

When he took office in 1978, Koch was handed a city on the brink of financial ruin. With a strange combination of fervent social liberalism and brutal fiscal conservatism, he slashed budgets, alienated some constituencies (especially African-Americans) while forging alliances with others. He also launched major rebuilding projects — the New York we see today is in many ways his vision, from the newly sanitized and corporatized Times Square to the gentrified Lower East Side.

Koch was never one to shy away from a camera, and Barsky has a wealth of archival footage to choose from — Koch on a street corner, parrying merrily with his citizens, or on television news, sharply dressing down an interviewer. Interviews with former staffers, political rivals and journalists who covered Koch offer context to his decisions — some masterful, some disastrous. Even those who opposed him seem to regard him with a kind of wonder.

But if “Koch” offers context, it never really offers explanation for what made him tick, what drove him. The closest Barsky gets is a quote from Koch on how a bigger-than-life city needed a bigger-than-life mayor. So was it all an act by a savvy career politician? If so, it was a remarkably consistent one, continued long after the cameras had turned away. Barsky also touches on the long-standing rumors that Koch was a closeted gay man, but handles it discreetly (and Koch shuts down the questioning with a “It’s none of their f—— business.”

Barsky intercuts the archival Koch with present-day footage of the former mayor, stumping for local candidates, going to fundraisers, arguing politics with family members at Yom Kippur, an elder statesman who seems ill at ease on the sidelines. Mellowing with age did not seem to be an option. Barsky takes us inside Koch’s apartment, and it’s a surprisingly spare place, the walls covered in photos and outsized caricatures of Koch.

What he truly saw in those portraits we’ll never know, but “Koch” is an engaging film about what New Yorkers saw in them. Had Koch lived to see it (he died this spring just a week before it opened in New York City), I think he would have found much to like and much to complain about. But he would have enjoyed the complaining, too.