There are certain ill-fated projects that loom large in comedy lore—as examples of terrible ideas, backstage calamity, deleterious studio interference, or evidence of an audience’s inability to recognize innovation in the moment. In 1961, the première of Jackie Gleason’s game show, “You’re in the Picture,” was so bad that Gleason began the second episode by offering an apology, noting that it “laid, without a doubt,” a bomb that “would make the H-bomb look like a two-inch salute.” In 1990, a British sitcom that imagined the domestic lives of Hitler and Eva Braun, called “Heil Honey I’m Home Home!,” was pulled after a single episode of unrivalled bad taste. In 1993, “The Chevy Chase Show,” which was heavily promoted by Fox as a late-night challenger to the other networks, was cancelled after just five weeks, and left behind such gems as Chase dancing stiffly onstage next to a denim-clad Goldie Hawn.

On this list, “The Dana Carvey Show,” which ran for seven episodes on ABC, in 1996, before being cancelled, occupies a special place. It was favored by a certain kind of comedy fan at the time, and, in the years since, thanks in large part to the subsequent success of many of the people who worked on it—Steve Carell, Stephen Colbert, Louis C.K., Robert Smigel, the filmmaker Charlie Kaufman, and others—has remained an object of fascination and discussion in the comedy world. In April, while appearing on Colbert’s “Late Night,” Louis C.K., who was the head writer of “The Dana Carvey Show” at the age of twenty-nine, recalled a story from the taping of the first episode, in which, infamously, Carvey, dressed as President Bill Clinton, fed an assortment of live baby animals from functioning synthetic teats on his chest. The sketch didn’t go well—just one such precarious moment on a show that Louis C.K. called “stressful.” Colbert was more specific: “I come around the corner, and you’re in the middle of the hallway openly weeping.”

Louis C.K. is not interviewed in “Too Funny to Fail,” a new documentary by Josh Greenbaum about “The Dana Carvey Show,” which was released this weekend, on Hulu. But the other principals appear, including Carvey, Carell, Colbert, and Smigel, as well as Heather Morgan and Bill Chott, both featured performers on the show, and Ted Harbert, the ABC executive who green-lighted and eventually cancelled the show. There is danger in probing mythology: when the actual footage is dusted off, cult failures can fail to live up to the hype. Colbert, recalling a bit about the awarding of the foreign-language Academy Award, calls it “possibly the most racist sketch ever committed to tape.” As with all sketch comedy, there is plenty about “The Dana Carvey Show” that is worth forgetting. But many of the surviving clips make a compelling case for the show as a noble experiment. And the documentary itself is a rare thing: a movie about comedy that is, itself, actually funny.

By the time Dana Carvey left “Saturday Night Live,” after the 1993 season, many of his characters had become firmly lodged in the cultural consciousness—Hans, the Church Lady, Garth, Ross Perot, President George H. W. Bush. The documentary skillfully captures the buzz over what Carvey would do next, showing clips of the comedian teasing his next project on late-night interviews and in magazine features. It all feels very nineties—the last gasp of the monoculture. Working with Smigel, his frequent collaborator on “S.N.L.,” Carvey pitched networks on a sketch show that would go where few such shows had ventured, and fewer succeeded: prime time. They landed at ABC, in a coveted Thursday slot after the family comedy “Home Improvement,” one of the top-rated TV shows at the time.

The problem, from the beginning, was one of misaligned priorities. Carvey and Smigel were assembling a band of “badass nerd pirates,” mostly undiscovered writers and performers, who would bring bleeding-edge sketch comedy to a big audience. ABC, meanwhile, wanted Carvey to play the “S.N.L.” hits—“Isn’t that special?” “Not gonna do it.” “Pump you up!” This tension was nicely encapsulated in the first sketch that opened the first show: Carvey, the master of impressions, played Bill Clinton—so far, so good, as the network saw it. But, then, an odd twist: Carvey opens his shirt to reveal the aforementioned false teats, and the baby animals feeding off of them. It was choose your adventure, uproarious, bold, unsettling, offensive, disgusting—and the audience apparently hated it. Citing real-time ratings, Harbert, the ABC executive, recalls that in its first few minutes the show lost millions of “Home Improvement” viewers who had hung around to check it out: “People ran for their remotes.”

From that point, the documentary posits, “The Dana Carvey Show” was doomed. Advertisers objected, and the network took a new interest in just what the weirdos it had hired were up to. Carvey, like Jackie Gleason three decades earlier, began the second episode by referring to the calamity of the previous week. But, rather than offer an apology, the show’s creators did what comedians do: they became oppositional and openly hostile to the people paying the bills, doubling down on the kind of comedy that would hasten its own demise. The show mocked the advertisers, and Smigel appeared in a recurring segment as a network executive demanding that the show become more appealing. There were the waiters nauseated by food; Grandma the Clown; “Skinheads from Maine”; pranksters who unknowingly prank themselves; and “The Ambiguously Gay Duo,” a cartoon short, later revived by Smigel to greater fame on “S.N.L.,” in which two superhero “special friends” drive a flesh-colored car shaped like a penis. The documentary generates great comedy by juxtaposing these oddities with clips and promotional material for the family-friendly content of the network’s other shows. After ABC cancelled the show, and declined to air its final completed episode, it replaced it with a rerun of “Coach.”

A popular show can’t become a cult favorite, and perhaps a show that has been elevated in memory because it failed never could have succeeded. And so, for a movie about a cancelled TV show, “Too Funny to Fail” is surprisingly cheerful, in large part owing to the fact that so many of the performers and writers on the show went on to such great comedy heights. The stakes, so high at the time that they brought Louis C.K. to tears, are lower now, and tragedy has been burnished into something more akin to pleasant melancholy. Yet, despite the collection of fond memories, and the film’s argument for the show as an incubator of talent and an expression of integrity, it’s clear that, for some, the scar still itches. “Hopefully I’ll watch this show, and I’ll look at the clips, and for a day I’ll feel good about it,” Smigel, who emerges as the most soulful of the show’s eulogizers, says, with a faint smirk. “Then back to abject regret.”