At first this seemed to be merely about how ventriloquism is a dying art, one rejected as cheesy by modern comedy audiences, but which the performers cling to because the puppets are their only means of expression. That was what A Ventriloquist's Story was about, but by the time an hour was up we saw there was more to it than that, and that that had more to it.
Conti has performed with her deliberately basic monkey puppet, Monk, for years with moderate success, persisting with an amusing act that I saw twice several years apart without noticing much progression. I didn't know she was personally invested in her trade, having learnt it from her former lover, the late Ken Campbell: actor, director, writer, comedian and restless dispenser of sideways wisdom about life and the creative process. Ventriloquism was just one theatrical medium he mercurially understood, experimented in and commanded.
The twinkling Campbell's moment of mainstream immortality came when he stole an episode of Fawlty Towers as Roger the anniversary party guest ("Well, one of them'll have to go – my money's on the carpet..."). But now he has a second lasting memorial in this programme, which was as much as anything about the painfully abiding feelings Conti has for Campbell – unresolved by his death in 2008 and her regret at things unsaid, spiced by the large age gap between them and their mentor/pupil relationship, and complicated slightly, at least for the viewers, by two brief glimpses of Conti's alive and present husband, a smiling man called Stan.
Ken bequeathed Nina his collection of ventriloquist dummies, giving Conti's story one of its many tart ironies: she'd since become convinced that her act had run its course, that she'd let Ken and Monk down and should give up. To close this long chapter permanently she took a trip to Kentucky, site of both a global ventriloquism convention and Vent Haven, a puppet museum for avatars who have lost their creators.
Over there, one bizarre but moving scene after another spilled out, as Conti took the idea of the puppet as a confessional outlet to extremes. Trapped in a featureless Travelodge-style room miles from home, and surrounded by puppets including a representation of Campbell himself, Conti argued with these other selves - the camera being another object that can somehow break down inhibitions other humans would only reinforce.
We heard how Conti, who you fancied is weighed down by self-awareness at all other times but was harnessing it here, dislikes her "falsely gauche" demeanour when she has to face the world without Monk. The pair went to the hotel bar, with Conti showing Monk her holiday reading: Problems of the Self by moral philosopher Bernard Williams.
Back in the room, with Conti drunk but Monk lucid, she explained how she didn't feel worthy of voicing Campbell's old puppets. Monk knew that that was not all. "You don't like this any more," he said of her habit of talking to and through dummies – the discipline that had dominated the last decade of her life. Conti tearfully shook her head.
A Ventriloquist's Story said profound things about the power of the performer's relationship with fictional characters. A bewilderingly beautiful sequence saw Conti take Gertrude Stein, a puppet of Campbell's which Conti voiced as a gentle surrogate grandmother, swimming in the hotel pool at night. The long-awaited visit to Vent Haven presented the bereaved dolls alongside photographs of their human partners in happier times, confirming that these puppets, these imaginary friends, these comfort blankets meant as much as any living companion.
Most startlingly, we saw Conti lying in bed beside the Campbell doll, giving it voice as it cruelly revealed exactly when and why her collaboration with Monk had begun. And, on Monk's own suggestion, there was a dry run for their separation in the form of a dramatic scene where he was run over and killed. Conti screamed and screamed. Was she acting? It didn't matter any more.
Eventually, Conti resolved to persist with ventriloquism. "Cool," said Monk.
Monk, Campbell and the macabre art of ventriloquism have clearly taken something from Conti. On the rare occasions when she spoke without letting a puppet interrupt her, her teeth were still clenched, as if to try to conceal the identity of the speaker. But out of that dark, twisted period has come this singularly affecting piece of television.
Before the credits rolled, Conti suddenly replaced herself with a Nina Conti puppet, putting it beside the wood-and-rubber ghost of Campbell on a balcony, in Kentucky, after dark. The Conti puppet told the Campbell puppet how much she'd loved him – like most of the film it was deeply emotional despite being, on the face of it, ludicrous. But then, as an old tape of Campbell had observed in voice-over, such things exist side by side.
A last surprise, not in the film: since A Ventriloquist's Story was made but before it was aired, Conti appeared on BBC3's topical news show, Russell Howard's Good News, with a slightly developed act that involved not just Monk but the established ventriloquist's variation of fitting a mask to a member of the audience and voicing them.
The clip got more than 2 million hits on YouTube last week. Who is this sure-footed overnight sensation, people asked. If only they knew.
Nina Conti - A Ventriloquist's Story is available on BBC iPlayer.