Many spoofs of the 1960s failed partly because they couldn’t top the inherent ridiculousness of their target. “The President’s Analyst,” starring James Coburn in the title role, surges past an ordinary hippie jaunt with assured Cold War nuttiness, a few gun-toting suburban liberals, and a zany conspiracy theory that may ring true to current Verizon customers. The 1967 caper, which Film Forum is reviving for one week beginning today, benefits from affable performances and playful direction, and the political satire doesn’t try to show off at being sharp or bemused.

The toothsome Coburn plays Dr. Sidney Schaefer, a healthily self-regarding and even-tempered Manhattan psychiatrist who is recruited to counsel the leader of the free world, who never appears on camera. Transplanted to a new house in Washington, D.C., by the powers that be — namely the “FBR” and “CEA” — he soon succumbs to the pressures of the post. The 24-hour availability that is required pales beside the deadly burden of his patient’s secrets. His paranoia blossoms.

So Sidney exits, pursued by spies (both ours and theirs). A self-proclaimed “typical American family” in New Jersey provides his first refuge, awash in “total sound” hi-fi and proudly announced values. After that, it’s on to those darn hippies by way of a love van parked outside the Café Wha? in Greenwich Village (which joins the Whitney Museum, the Statue of Liberty, and other city locations in Cinemascope glimpses). The rest of the movie is whisked away by espionage shenanigans that reveal American agent Don and his Soviet counterpart Kropotkin (the comics Godfrey Cambridge and Severn Darden, respectively) to be “how-ya-been” colleagues.

Coburn, coming off the “Flint” James Bond spoofs (1966’s “Our Man Flint” and 1967’s “In Like Flint”) entertains mightily when delivering the insanely level-minded rationalization for psychoanalysis. Sidney marvels at the psychological ramifications of the covert-ops lifestyle: Government assassins, after all, can “vent aggressive feelings by actually killing someone.” The casualness of Cambridge and Darden’s rival spies picks up on this strain of amiably normalized insanity to even better effect.

Cambridge, Darden, and Joan Darling (as Sidney’s girlfriend) were all veterans of director Ted Flicker’s award-winning Village improv troupe, the Premise. The next well-known project by Mr. Flicker was the ubiquitously rerun cop sitcom “Barney Miller” (also set in the Village), which earned the now-ex-filmmaker what his sculpture-filled Web site calls “getaway money.” Pop art and some sculpture figure, in fact, in a few mild sight gags in “The President’s Analyst.”

The free brand of political satire from Mr. Flicker’s Premise days apparently didn’t sit will with one of the targets. The FBI is represented as a black-suited squad of agents, none of whom significantly exceed the height of their runty, moralizing leader. When the film was released, FBI chief J. Edgar Hoover expressed displeasure by proxy and issued warnings to the studio; this story tends to gloss over the dismaying reality of his having vetted the script in the first place. It’s a sinister footnote to a film that otherwise stands on the flip side of President Nixon and the darker treatment of paranoia in movies of the 1970s. (The original use of “FBI” and “CIA” would, in fact, be redubbed before release.)

“The President’s Analyst” has the added perk over similar period items, such as Blake Edwards’s “The Party,” of not imposing its meandering too heavily on the viewer. When Sidney, done up in red shades and vest, blisses out in a field with a flower child, it’s paired with the eloquent gag of his successive assassins killing one another a few feet away. (It’s harder to know, though, how to take Sidney’s feeling-groovy walk through the city after landing his new job.) All in all, it’s a worthy summer diversion that happens to hide its age well with some far-out prescience, and one that sets up Film Forum for another revival of presidential lows: What about a seesaw deep into the next decade’s mind-set with Robert Aldrich’s postelection doomsday thriller “Twilight’s Last Gleaming”?

Through June 12 (209 W. Houston St., between Sixth Avenue and Varick Street, 212-727-8110).