This paper examines the Gricean view that quality maxims take priority over other conversational maxims. It is shown that Gricean conversational implicatures are routinely inferred from utterances that are recognized to be untruthful. It is argued that this observation falsifies Grice's original claim that hearers assume that speakers are obeying other maxims only if the speaker is assumed to be obeying quality maxims, and furthermore the related claim that hearers assume that speakers are being cooperative only to the extent that they assume they are being truthful.