It'd have been an unconventionally rose-tinted approach for the usually assidious Gibney; several talking heads in the film's 2013 sections, including Armstrong's former teammate Frankie Andreu and his wife, dogged Armstrong persecutor Betsy, openly express their amused dismay that he ever considered making it. But Gibney admits that, four years ago, he fell hook, line and sinker for the so-called Armstrong lie, and has had to perform an about-face on this entire project and his reason for making it.

That can't be an easy admission to make: the resulting peevishness of "The Armstrong Lie" makes it at once one of Gibney's most humanly compelling works, and one of his more rhetorically inconsistent, as the film unavoidably slides between interview footage from before and after the fact that pursues very different intelligence and emotion.

Armstrong is a chilly but willing interview participant in footage filmed this spring, in the aftermath of his irreversibly comprehensive Oprah confession, but strangely, he never seems more contrite than in intimate, conversational footage with Gibney immediately after his 2009 Tour defeat, in which he apologizes for losing and thereby denying Gibney's film its triumphant ending. He's not joking, either. All along, Armstrong's chief skill -- well, maybe not his chief one; he's still a half-decent cyclist -- has been as a builder of personal narrative. If he's unrewardingly bland and unforthcoming in what should be the 'gotcha!' stages of Gibney's new-model film, it's because, with his personal and professional reputation still in fresh tatters, he hasn't located the next narrative yet.

Rumsfeld, by contrast, built an entire career on being unrewardingly bland and unforthcoming -- as "The Unknown Known" reminds us with frequent flashbacks (boxed, as we saw them, within a turn-of-the-century television screen) to his famous White House press conferences, where he deflected one question after another with breathtakingly smarmy poise and patter. He may not have fooled onlookers into believing he knew significantly more than they did -- or, in the case of his recurring gaffe over WMDs, that his professed ignorance was any more considered than theirs -- but his watery confidence was intimidating on a human level. It's hard to argue productively with someone who may indeed have nothing to hide, who genuinely appears to believe his stubborn, transparently unsustainable convictions.

That enigma -- whether Rumsfeld has ever doubted his public frontage, whether his most contentious war strategies were born of profound belief or tactical stopgapping -- is one Errol Morris doesn't really come close to penetrating in "The Unknown Known." A typically handsome, charcoal-hued effort, it has plainly been conceived as a structural and thematic bookend to "The Fog of War," Morris' Oscar-winning interrogation of another former Defence Secretary, Robert McNamara, with a lot on his conscience. In his smooth but insistent way, Morris cracked McNamara: there was no cathartic mea culpa on his Vietnam decision-making, of course, but his open engagement and reasonably candid self-evaluation was victory enough.

If Morris was hoping to tease out this degree of consideration in Rumsfeld, he's out of luck. Pristinely power-suited, with his high, even vocal tone as intact as if he'd just fielded another press conference, Rumsfeld sits before Morris' classically direct camera like a man out to pass a test, barely pausing for thought before batting off the interviewer's questions with unfazed, occasionally bored politeness. "I'm not an obsessive person," he responds dully, at the first hint of a rise in Morris' tone. "I'm cool and measured."

That may be a smug, unendearing start to an interview, but damn it, the man's not wrong. "Everything seems amazing in retrospect," he drawls, sounding resolutely unamazed, as Morris tries in vain to draw him into battle on such matters as the conflation of Saddam Hussein and Osama Bin Laden in the US imagination ("Oh, I don't think so"), those confounding weapons of mass destruction ("The absence of evidence is not evidence of absence") and the human violations of Guantanamo Bay ("Things occur that shouldn't occur"). Most lines of enquiry are punctuated with that tightly sealed smile.

Guy Lodge is a South African-born critic and sometime screenwriter. In addition to his work at In Contention, he is a freelance contributor to Variety, Time Out, Empire and The Guardian. He lives well beyond his means in London.