The subject of irony in film is a problematic one, in no small measure because of the assumption of referentiality in what is shown onscreen. I examine a form of irony that is tied to undecidability and use it to analyze La moustache (2005), which is a cinematic exploration of the possibilities for creating undecidability and its attendant tensions, exemplifying how irony may be visually communicated. Carrère's film moves into the domain of irony through a wide-ranging critique worked out through discordance.